Archive for March, 2009

PMO negotiator travels abroad to pursue Shalit deal

March 29, 2009
PMO negotiator travels abroad to pursue Shalit deal
By Barak Ravid, Haaretz Correspondent
Tags: Israel news, Ofer Dekel
Prime Minister Ehud Olmert’s special negotiator for prisoner affairs Ofer Dekel traveled abroad to an unspecified destination Saturday to further pursue a prisoner exchange agreement that would see captive Israeli soldier Gilad Shalit released.

Shalit was kidnapped by Gaza militants in a cross-border raid in 2006. Hamas, the rulers of the Gaza Strip, have demanded the release of hundreds of Palestinian prisoners in exchange for the Israel Defense Forces soldiers’ freedom. Negotiations between Israel and Hamas, mediated by Egypt, broke down earlier this month over the identities of several Palestinian prisoners and the deportation of some prisoners out of Gaza following their release.

However, the Prime Minister’s Bureau issued a statement late Saturday insisting that the prisoner exchange negotiations had not been renewed, and that Dekel had not traveled to Egypt.

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“Hamas has not submitted a new prisoner list, and therefore the negotiations have not been renewed,” the statement said.

Egyptian sources said that “there is no longer time to reach an agreement during the term of the incumbent government, but maybe one will be reached with the government led by Benjamin Netanyahu.”

Earlier, parents of terror victims wrote to Olmert and to Defense Minister Ehud Barak, asking them not to release Palestinian prisoners who had killed Israelis.

The head of Hamas’ military wing in the Rafah area of the Gaza Strip, Ra’ad al-Atar said on the division’s Web site that his organization will abduct more Israeli soldiers now that the exchange deal has collapsed. Security officials believe Atar was one of the architects of the military operation that ended with Shalit’s abduction.

On Sunday, Dekel told Egyptian mediators that Israel would agree to resume the negotiations only if Hamas agrees to submit a new list of prisoners for Israel’s consideration.

Senior Egyptian official Mohammed Ibrahim was in Israel on Tuesday and Wednesday to work on the deal, and met with Dekel, Shin Bet security service chief Yuval Diskin and other officials. Ibrahim, who is Egyptian intelligence chief Omar Suleiman’s deputy, has coordinated the Shalit talks for Egypt.

Ibrahim tried to convince Israel to soften its “red lines.” However, an Israeli source said that Jerusalem rejected this demand.

Israel says it has agreed to release 325 of the 450 prisoners Hamas has demanded by name, but is unwilling to release the remaining 125. It is therefore insisting that Hamas present a new list of names from which Jerusalem could choose the remaining 125 to round out the total, to which it has already agreed.

Related articles:

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  • Hamas: We want to finalize Shalit deal as soon as possible
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    March 25, 2009
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    March 24, 2009 by Peter Ekman
    Category: Albums (and EPs)

    mazesNumerology never did you any favors, safe to say, but dig this big crux: Mazes spin off from The 1900s, the psychish Chicago poppers formed in 2004 and last seen orbiting the blogosphere. (Not 1990s, mind you, those rakish Scotsmen [2006] with Yummy Fur wafting through their veins.) The 1900s? Seven-piece. Mazes? Just three.

    Edward Anderson and Caroline Donovan shed the wall-of-twee plenitude The 1900s do so well, and in tandem with Charles D’Autremont weave a markedly looser “mid-fi” collection hatched in that venerable, nebulous American thirdspace: bedrooms, basements, and the odd studio under duress. It’s a thoroughly pleasing ride, with twangy divagations here and there — just echoes, really: see, inter alia, “Heather on Heather” — but for the most part is a clear-sightedly eclectic popfest, surprising but never jarring.

    Anderson’s voice isn’t distinctive, but his steady delivery, his allergy to overt histrionics, keeps the layered instrumentation at center stage. What wags will doubtless call lush, shimmering, haunting, strikes me as just subtle. Each track wears its thick adornment lightly, and it never feels fussy, just mindful.

    The press machine says Mazes channel New Zealand — i.e. Flying Nun, 1981 A.D.; The Chills, The Clean, and all — but I’m hearing a synthesis and gentle reconfiguration of ’90s archetypes above all. When the Farfisa cuts through on “Cat State Comity,” assertive but not strutting, a baroque little foil to the vocal melody, they’re speaking Aislers Set. Similarly on “Love to Lay,” as close to pop perfection as it comes: organ meat lines the skeletal form, nearly motorik in its hushed insistence. Vocal lines dive and weave, setting up daring chord changes that don’t disorient so much as enlighten. The lazy boy–girl act recalls the light-hearted Yo La Tengo that comes out on Fakebook; post-surf amuse-bouches fall in with the Crabs, the K also-rans, or the supple, spare guitar duels proffered lately by, say, Real Estate.

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    Thursday, March 19, 2009

    Revolutionary Mazes

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    Wednesday, March 18, 2009

    Blivet and Nitnoid

    BLIVET AND NITNOID

    [Q] From John McWilliams: “I am an engineer and have used the words blivet and nitnoid all my professional life, but I’m not sure if they are real words. To me, a blivet is some small amorphous shape like a blob. A nitnoid is a small mechanical device of little importance as in, ‘that nitnoid keeps the belt tight’. Any help?”

    [A] Blivet is by far the better known of the two words and dictionaries of American slang suggest it dates back to American servicemen in World War Two. It is frequently said to be any small, useless, unnecessary or superfluous thing. It looks like a mixture of blip and widget, though your definition suggests that it might instead be from blip plus rivet.

    It’s often described as ten pounds of horse manure in a five-pound bag (though the quantities vary between tellers) and the excuse to retell that “explanation” to a naive onlooker is often the reason for using the word. I am told that in the 1950s the term could be used to describe a person who was either self-important and full of himself or grossly overweight, for whom this description was all too apt.

    When this piece first appeared, many subscribers mentioned that they knew blivet as the name of an impossible two-pronged trident thingy, otherwise known as the Devil’s pitchfork. It is sometimes said that the name derives from “believe it”, which I don’t. Other subscribers remember blivet as a military term for rubberised bladders that were used by various air forces for holding fuel at temporary locations, usually small airstrips. Once drained, the bags would go flat and be easily stored until required for use elsewhere.

    Your other word, nitnoid, is clearly also American slang, though it’s new to me and there’s nothing in any of my books to tell me its origin (the earliest example I’ve found is from 1992, but it clearly must be significantly older). There are references to it online that suggest it can be a niggling small matter of no consequence, or something that’s nit-pickingly frustrating, or a pedantic person intent on squashing the life out of some subject by considering every detail. This suggests a derivation from nit plus the suffix -oid to indicate something of a given nature (plus, to be nitnoid about the matter, an interpolated n to make it easier to say, and perhaps a trace more humorous). Examples include “he has written a book chock full of nitnoid detail”, and “this man is a nitnoid perfectionist”. A rare example in print appeared in the Atlanta Constitution in September 2001: “We need to appreciate every moment we have with each other and just be nicer and not get lost in the nitnoid frustrations of life.” Interestingly, though this is clearly in the same ball park as your example, none of the instances I’ve found have quite the same sense.

    It was confidently said by many subscribers to derive from the Thai nit noi, meaning “just a little”, with the suggestion that it was brought back to the USA by servicemen returning from the Vietnam war. I can’t find evidence to directly confirm or deny this one, though the gap between the Vietnam era and the first appearance of the word might count against its being the source.

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    Monday, March 16, 2009

    Mazes of Gilad Shalit, Woody Allen, Michalangelo’s David

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    mazes

    March 25, 2009
    Read reactions to this story

    Mazes – Mazes

    Read “Mazes-Mazes” Article from the source – Click here!

    March 24, 2009 by Peter Ekman
    Category: Albums (and EPs)

    mazesNumerology never did you any favors, safe to say, but dig this big crux: Mazes spin off from The 1900s, the psychish Chicago poppers formed in 2004 and last seen orbiting the blogosphere. (Not 1990s, mind you, those rakish Scotsmen [2006] with Yummy Fur wafting through their veins.) The 1900s? Seven-piece. Mazes? Just three.

    Edward Anderson and Caroline Donovan shed the wall-of-twee plenitude The 1900s do so well, and in tandem with Charles D’Autremont weave a markedly looser “mid-fi” collection hatched in that venerable, nebulous American thirdspace: bedrooms, basements, and the odd studio under duress. It’s a thoroughly pleasing ride, with twangy divagations here and there — just echoes, really: see, inter alia, “Heather on Heather” — but for the most part is a clear-sightedly eclectic popfest, surprising but never jarring.

    Anderson’s voice isn’t distinctive, but his steady delivery, his allergy to overt histrionics, keeps the layered instrumentation at center stage. What wags will doubtless call lush, shimmering, haunting, strikes me as just subtle. Each track wears its thick adornment lightly, and it never feels fussy, just mindful.

    The press machine says Mazes channel New Zealand — i.e. Flying Nun, 1981 A.D.; The Chills, The Clean, and all — but I’m hearing a synthesis and gentle reconfiguration of ’90s archetypes above all. When the Farfisa cuts through on “Cat State Comity,” assertive but not strutting, a baroque little foil to the vocal melody, they’re speaking Aislers Set. Similarly on “Love to Lay,” as close to pop perfection as it comes: organ meat lines the skeletal form, nearly motorik in its hushed insistence. Vocal lines dive and weave, setting up daring chord changes that don’t disorient so much as enlighten. The lazy boy–girl act recalls the light-hearted Yo La Tengo that comes out on Fakebook; post-surf amuse-bouches fall in with the Crabs, the K also-rans, or the supple, spare guitar duels proffered lately by, say, Real Estate.

    Perhaps Mazes isn’t as freewheeling as they say — everything works in deference, even if not outright submission, to a cunning, capacious logic — but it supplies a certain levity that higher-strung perfectionist pop often manifestly lacks. The stars align, maybe, and it all adds up.

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    Sunday, March 22, 2009

    BLIVETs

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    Blivet Maze – Optical illusion maze of an impossible object.
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    They that mistake life’s accessories for life itself are like them that go too fast in a maze: their very haste confuses them

    Seneca quotes (Roman philosopher, mid-1st century AD)

    Maze of Monkey Illusion – 2009
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    “Boris Podolsky: James! How’s the rat business?

    James Moreland: Well, actually it’s mostly students I’m experimenting on now.

    Kurt Godel: My God, the mazes must be enormous.


    IQ quotes (Movie)

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    The man of character, sensitive to the meaning of what he is doing, will know how to discover the ethical paths in the maze of possible behavior.

    Earl Warren quotes (American Republican Politician and Judge, 18911974)

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    Barak Obama Maze – 2009

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    Real obstacles don’t take you in circles. They can be overcome. Invented ones are like a maze.
    Barbara Sher

    Maze of 3D Impossible Object – 2009 – By Yonatan Frimer
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    It is easier to penetrate your audience with one sharp, clean point or idea, thand with a maze of half-baked unremarkable, uninspiring ideas that will never motivate or be remembered.

    ~ Stavros Cosmopulos quotes

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    Happiness, that grand mistress of the ceremonies in the dance of life, impels us through all its mazes and meanderings, but leads none of us by the same route.

    Charles Caleb Colton quotes (English sportsman and writer, 1780-1832)

    Maze of Barak Obama, profile view – 2009
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    When I was in New York it was like a maze, a rat maze, going from one little box to another little box and passing through passageways to get from one safe haven to another.
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    Maze – Kong 2006
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    Life is a maze in which we take the wrong turn before we have learnt to walk

    Cyril Connolly quotes (English critic and editor, 1903-1974)



    Maze King, of Rock N Roll, Elvis
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    Elvis Maze – By Yonatan Frimer

    “They that mistake life’s accessories for life itself are like them that go too fast in a maze: their very haste confuses them.”

    ~ Seneca quotes






    Matrix Maze – Keanu Reeves, Neo
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    The maze … was such a mind-altering and life-changing experience. … My gosh, I mean for something that’s pretend it changes your viewpoint on life,

    ~ John Travolta quotes


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    Thursday, March 19, 2009

    Revolutionary Mazes

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    Wednesday, March 18, 2009

    Blivet and Nitnoid

    BLIVET AND NITNOID

    [Q] From John McWilliams: “I am an engineer and have used the words blivet and nitnoid all my professional life, but I’m not sure if they are real words. To me, a blivet is some small amorphous shape like a blob. A nitnoid is a small mechanical device of little importance as in, ‘that nitnoid keeps the belt tight’. Any help?”

    [A] Blivet is by far the better known of the two words and dictionaries of American slang suggest it dates back to American servicemen in World War Two. It is frequently said to be any small, useless, unnecessary or superfluous thing. It looks like a mixture of blip and widget, though your definition suggests that it might instead be from blip plus rivet.

    It’s often described as ten pounds of horse manure in a five-pound bag (though the quantities vary between tellers) and the excuse to retell that “explanation” to a naive onlooker is often the reason for using the word. I am told that in the 1950s the term could be used to describe a person who was either self-important and full of himself or grossly overweight, for whom this description was all too apt.

    When this piece first appeared, many subscribers mentioned that they knew blivet as the name of an impossible two-pronged trident thingy, otherwise known as the Devil’s pitchfork. It is sometimes said that the name derives from “believe it”, which I don’t. Other subscribers remember blivet as a military term for rubberised bladders that were used by various air forces for holding fuel at temporary locations, usually small airstrips. Once drained, the bags would go flat and be easily stored until required for use elsewhere.

    Your other word, nitnoid, is clearly also American slang, though it’s new to me and there’s nothing in any of my books to tell me its origin (the earliest example I’ve found is from 1992, but it clearly must be significantly older). There are references to it online that suggest it can be a niggling small matter of no consequence, or something that’s nit-pickingly frustrating, or a pedantic person intent on squashing the life out of some subject by considering every detail. This suggests a derivation from nit plus the suffix -oid to indicate something of a given nature (plus, to be nitnoid about the matter, an interpolated n to make it easier to say, and perhaps a trace more humorous). Examples include “he has written a book chock full of nitnoid detail”, and “this man is a nitnoid perfectionist”. A rare example in print appeared in the Atlanta Constitution in September 2001: “We need to appreciate every moment we have with each other and just be nicer and not get lost in the nitnoid frustrations of life.” Interestingly, though this is clearly in the same ball park as your example, none of the instances I’ve found have quite the same sense.

    It was confidently said by many subscribers to derive from the Thai nit noi, meaning “just a little”, with the suggestion that it was brought back to the USA by servicemen returning from the Vietnam war. I can’t find evidence to directly confirm or deny this one, though the gap between the Vietnam era and the first appearance of the word might count against its being the source.

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    Monday, March 16, 2009

    Mazes of Gilad Shalit, Woody Allen, Michalangelo’s David

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    Maze Pop Art: Awesome!

    March 22, 2009

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    Have a look at our maze collection. Enjoy.

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    Maze of an Olympic Pool –  Y.Frimer Mazes
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    Please contact the maze artist if you’d like to use any of these mazes in your publication or paper.

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    March 19, 2009

    Random Maze

    Here is a random maze I have generated by Monte Carlo.  Can you find the way out?

    In reality, a random maze would be much more convoluted than the above example.  Such mazes are less pleasing to the eye. In the case above a maze consisting of walls that spiral from the origin was generated, and then subjected to a Monte Carlo simulation for a short time (before the maze would randomize completely).

    Random Tree:

    A maze is a special kind of random tree:  in particular, it is a spanning tree of a square in the square lattice (such a maze would have only one way out from the center).  Below is a random tree in the square lattice.


    Towards the limiting random lattice tree

    If the number of edges in the tree above should be multiplied, while the length scale is shrunk appropriately, a limiting random tree will be seen.  In the picture below there are 10000 edges, each too small to be seen here, in a lattice tree generated by a Monte Carlo program.  The tree begins to appear like a fractal object.  The existence of a scaling limit is known in high dimensions (above 8).  There is general consensus that it also exists in dimensions below 9.


    Random Disks

    The interior of a closed loop in the square lattice (or a polygon) is a Disk.  In this example, a square lattice polygon was randomized by subjecting it to a Metropolis Monte Carlo algorithm.  The interior of the polygon is a disk.

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    ************************

    Part 3 – Tile-Based Graphics, and Maze Creation


    Often in game creation it becomes necessary to create multiple sets of game graphics and background images which contain similar details and repeating elements. It may be for a HUGE outdoor overhead map for a role-playing game showing landmarks, hills, trees, grass, monsters, etc., or as in our case, a bunch of similarly-constructed mazes, or whatever. As game designers and programmers, we need to be able to store, manipulate, and recreate these in our game, using as few graphic, memory, and hard disk storage resources as possible.

    One common way of doing this is called “Tokenizing” the image. Instead of saving and loading all the images we could possibly need for our game, we break the image down into a small number of replicable parts – a set of graphic pieces that we can arrange to create the image we need when we need it. Usually, most pieces in this set are the same size, and will match up against other pieces in the set. The graphic pieces are generally called “tiles.” The graphic screens are stored as a matrix of alphanumeric characters, called “tokens,” with each character in the matrix corresponding to one of the graphic tiles.

    Here are the mazes I have created so far for Snack Attack!

    The first “maze” is for the About this Game screen. The ghosts chase Snacky around the About this Game text. The next maze (top, middle) is the original Pacman maze, resized to fit our game window. The next four mazes (the red, purple, green, and brown ones) are the original mazes from Ms.Pacman, and the last two I found in hacked MsPacman roms on the net.

    Looking at the mazes, you’ll see that they all contain similar elements – rounded ends, right angle bends, segments that are the same length, etc.. To create these mazes, I took screen shots of the Pacman, et al, mazes and cut them up into 24 chunks. These 24 pieces arranged carefully, can recreate any maze a Pacman game can run.

    Once I knew what the pieces needed to look like, I had to determine how to create a set we can use for our game. I had to make some creative and technical decisions to make the game easier to do and to make the mazes “fit” in our game window.

    The mazes in the Pacman Arcade game are 1.5 times as tall as they are wide, and our game window is roughly square in mode 19, which has a 3:4 aspect ratio. In the Original, the maze borders are thinner than the maze obstacles, and the vertical spacing between obstacles alternates between high and short as we go from top to bottom in the maze. To limit the number of tiles we’d need and to make maze creation and AI programming easier, I decided to have one set of tiles for everything, and to make all the tiles the same size. Notice our borders and obstacles are the same thickness.

    After a couple hours of tweaking, I determined the “correct” matrix size for our game is 19×22, with tiles that are 12×8 pixels in size. My primary criteria was being able to reproduce the original Pacman maze using uniform-sized tiles, and this maze needed to fit in a square game window as close as possible to the screen size we have. Our game window is about 8 pixels shorter than my other games, so I added the light blue border box around the game window, centered it, and adjusted the size of our feedback window to make it balance better. Since our Maze tiles are 12×8, for consistency sake, I set the graphics size for all the moving sprites to also be 12×8. This really is arbitrary, but it makes keeping track of them easier. Another upshot of having 12×8 tiles is we end up with about 1/3 fewer dots than the original.

    Here is our minimum tile set:

    Notice that our tile set is not colored. In the game we need to draw the mazes in different colors, so our tile set here is black, white, and gray. When we draw the maze we’ll color the white and gray pixels in each tile to the outline and interior color, respectively. Here I’m showing you the 2D “arcade” tile set, because it’s easier to see how it fits together. I have a more solid, 3D pipes-look tile set in 10 colors that will be included in the final version of the game. It was constructed the same way, only I processed each tile in photoshop to make it look 3D like. We’ll have a game option to choose between the two tile sets.

    Our tile set contains a few extra tiles to correspond with new features we’ve added to the game. The 6 images along the bottom row are doors. The first two are doors for the penalty box. In Pacman and MsPacman, the penalty box is always in the same place, in the same orientation. The reason I think is that they needed to hardcode the location so that the ghost’s eyes can find their way back to the box so that the ghosts can respawn when we kill them. For our game, we can just have the eyes target the Penalty box door, and they’ll always find it, so we can put the Penalty box anywhere in the maze and it can have a vertical orientation if we want it to. Therefore I included a Horizontal and Vertical Penalty box door.

    The next two doors are Ghost-Only doors. Snacky can’t go through them. We may want to make passages for the ghosts so they can ambush Snacky. The last two doors are Snacky-only doors. We may want to block the ghosts from certain Snacky-safe escape routes.

    Included in the tile set is a Dot, so we can place the dots only where we want them. Similarly, we can place energizers anywhere we want, and since Euphoria is flexible in redimentioning sequences, we can have as many of them in the maze as we’d like.

    Our game will determine the starting positions and number of ghosts from the maze definitions, so we can place as many ghosts as we want to, anywhere in the maze. We MUST have a penalty box, with a Penalty Box Door, but we can have the ghosts start from anywhere.

    Snacky’s starting position will also be determined by the maze definition. We can start the game with Snacky anywhere we want.


    Tokenizing the maze
    Ok, so we have a tile set that we can use to construct any maze we can think of. So, how do we do it? I told you before that we want to represent the maze as a matrix of alphanumeric characters with each character corresponding to a tile in the tile set. Our mazes are 19×22 tiles big, and thus they can be represented by a matrix containing only 418 characters. That’s pretty tight. Storing the mazes as a GIF image is 6 times as large and GIFs are compressed pretty tightly.

    How do we choose the tokens for each tile? Arbitrarily. You can make any alphanumeric character represent any tile you want. I usually try to go for characters that look kinda like the tile, so when I look at the text representation, I can tell what the maze is. Here is a maze from Snack Attack! And it’s corresponding text representation:

    ( is an upper left corner,
    ) is an upper right corner,
    [ is a lower left corner,
    ] is a lower right corner,
    < is a left ending horizontal piece,
    > is a right ending horizontal piece.
    O is an energizer and o is a dot.
    C is the player’s starting position – because C kinda looks like Snacky.
    M is a Ghost (M for Monster)
    P is the Penalty Box door.
    = is a horizontal piece.

    You get the idea. When I run out of characters that look like tiles, I just start picking letters and symbols until I run out of tiles.

    I store all the levels in the game (in the maze order shown above) back to back in one long sequence of sequences of sequences. Levels is all of the mazes, Levels[1] is the about maze, Levels[3][4][5] is the token at position 5,4 in the second level.(the red one in the image above – third maze in the sequence)

    For our purposes, I have created a handy, dandy maze editor we can use to create the mazes. You click on the tile you want and then place it in the game window. The program indexes into the maze definition sequence and places the right token in the right place automagically.

    If you haven’t yet downloaded my version of our course project, Snack Attack!, do it now, and play it a million times to get an idea for the game.

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    Amazing Challenge I

    By Shawn Olson

    Posted on 12.18.03

    As a kid I used to draw mazes all the time. Sometimes I would draw a couple dozen mazes and tape them together, so that the entire maze was twenty feet long laid out. I hadn’t made any mazes in a long time, so I decided it’s time to get back in the habit. Here is the first maze in my series of Amazing Challenges. Enjoy.

    Click the image to view the maze full-size.

    shawn's amazing challenge 1

    Copyright © 2003-2009 by Shawn Olson.

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    Help the Monarch butterfly fly south for the winter.

    Back to Fall mazes.

    Be sure to visit our main printables index for more fun including our Fall coloring pages, word puzzles and check out our great Fall crafts!

    Click here for printable version

    More fun printables and activities to enjoy:

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    Maze cartoon

    Maze Classification

    Mazes in general (and hence algorithms to create Mazes) can be organized along seven different classifications. These are: Dimension, Hyperdimension, Topology, Tessellation, Routing, Texture, and Focus. A Maze can take one item from each of the classes in any combination.

    Dimension: The dimension class is basically how many dimensions in space the Maze covers. Types are:

    • 2D: Most Mazes, either on paper or life size, are this dimension, where it’s always possible to display the plan on the sheet of paper and navigate it without overlapping any other passages in the Maze.
    • 3D: A three dimensional Maze is one with multiple levels, where (in the orthogonal case at least) passages may go up and down in addition to the four compass directions. A 3D Maze is often displayed as an array of 2D levels, with “up” and “down” staircase indicators.
    • Higher dimensions: It’s possible to have 4D and higher dimension Mazes. These are often rendered as 3D Mazes, with special “portals” to travel through the 4th dimension, e.g. “past” and “future” portals.
    • Weave: A weave Maze is basically a 2D (or more accurately a 2.5D) Maze, but where passages can overlap each other. In display it’s generally obvious what’s a dead end and what’s a passage that goes under another. Life size Mazes that have bridges connecting one portion of the Maze to another are partially Weave.

    Hyperdimension: The hyperdimension class refers to the dimension of the object you move through the Maze, as opposed to the dimension of the Maze environment itself. Types are:

    • Non-hypermaze: Virtually all Mazes, even those in higher dimensions or with special rules, are normal non-hypermazes. In them you work with a point or small object, such as a marble or yourself, which you move from point to point, where the path behind you forms a line. There’s an easily countable number of choices at each point.
    • Hypermaze: A hypermaze is where the solving object is more than just a point. A standard hypermaze (or a hypermaze of the 1st order) consists of a line where as you bend and move it the path behind it forms a surface. A hypermaze can only exist in a 3D or higher dimension environment, where the entrance to a hypermaze is also a line instead of a point. A hypermaze is fundamentally different since you need to be aware of and work with multiple parts along the line at the same time, where there’s nearly an infinite number of states and things you can do with the line at any time. The solving line is infinite, or the endpoints are fixed outside the hypermaze, to prevent one from crumpling the line into a point, which could then be treated as a non-hypermaze.
    • Hyperhypermaze: Hypermazes can be of arbitrarily high dimension. A hyperhypermaze (or a hypermaze of the 2nd order) increases the dimension of the solving object again. Here the solving object is a plane, where as you move it the path behind you forms a solid. A hyperhypermaze can only exist in a 4D or higher dimension environment.

    Topology: The topology class describes the geometry of the space the Maze exists in. Types are:

    • Normal: This is a standard Maze in Euclidean space.
    • Planair: The term “planair” refers to any Maze with an abnormal topology. This usually means connecting the edges of the Maze in interesting fashions. Examples are Mazes on the surface of a cube, Mazes on the surface of a Moebius strip, and Mazes that are equivalent to being on a torus with the left and right sides wrapping and the top and bottom wrapping.

    Tessellation: The tessellation class is the geometry of the individual cells that compose the Maze. Types are:

    • Orthogonal: This is a standard rectangular grid where cells have passages intersecting at right angles.
    • Delta: A Delta Maze is one composed of interlocking triangles, where each cell may have up to three passages connected to it.
    • Sigma: A Sigma Maze is one composed of interlocking hexagons, where each cell may have up to six passages connected to it.
    • Theta: Theta Mazes are composed of concentric circles of passages, where the start or finish is in the center, and the other on the outer edge. Cells usually have four possible passage connections, but may have more due to the greater number of cells in outer passage rings.
    • Upsilon: Upsilon Mazes are composed of interlocking octagons and squares, where each cell may have up to eight or four possible passages connected to it.
    • Zeta: A Zeta Maze is on a rectangular grid, except 45 degree angle diagonal passages between cells are allowed in addition to horizontal and vertical ones.
    • Omega: The term “omega” refers to most any Maze with a consistent non-orthogonal tessellation. Delta, Sigma, and Theta Mazes are all of this type, as are many other arrangements one can think up, e.g. a Maze composed of pairs of right triangles.
    • Crack: A crack Maze is an amorphous Maze without any consistent tessellation, but rather has walls or passages at random angles.
    • Fractal: A fractal Maze is a Maze composed of smaller Mazes. A nested cell fractal Maze is a Maze with other Mazes tessellated within each cell, where the process may be repeated multiple times. An infinite recursive fractal Maze is a true fractal, where the Maze contains copies of itself, and is in effect an infinitely large Maze.

    Routing: The routing class is probably the most interesting with respect to Maze generation itself. It refers to the types of passages within whatever geometry defined in the categories above.

    • Perfect: A “perfect” Maze means one without any loops or closed circuits, and without any inaccessible areas. Also called a simply-connected Maze. From each point, there is exactly one path to any other point. The Maze has exactly one solution. In Computer Science terms, such a Maze can be described as a minimal spanning tree over the set of cells.
    • Braid: A “braid” Maze means one without any dead ends. Also called a purely multiply connected Maze. Such a Maze uses passages that coil around and run back into each other (hence the term “braid”) and cause you to spend time going in circles instead of bumping into dead ends. A well-designed braid Maze can be much harder than a perfect Maze of the same size.
    • Unicursal: A unicursal Maze means one without any junctions. Sometimes the term Labyrinth is used to refer to constructs of this type, where “Maze” means a puzzle where choices are involved. A unicursal Maze has just one long snake-like passage that coils throughout the extent of the Maze. It’s not really difficult unless you accidentally get turned around half way through and make your way back to the beginning again.
    • Sparseness: A sparse Maze is one that doesn’t have a passage through every cell, where some are left uncreated. This amounts to having inaccessible locations, making this somewhat the reverse of a braid Maze.
    • Partial braid: A partial braid Maze is just a mixed Maze with both loops and dead ends in it. The word “braid” can be used quantitatively, where a “heavily braid Maze” means one with many loops or detached walls, and a “slightly braid Maze” means one with just a few.

    Texture: The texture class is subtle, and describes the style of the passages in whatever routing in whatever geometry. They’re not really on/off flags as much as general themes. Here are several example variables one can look at:

    • Bias: A biased Maze is one with straightaways that tend to go in one direction more than the others. For example, a Maze with a high horizontal bias will have long left-right passages, and only short up-down passages connecting them. A Maze is usually more difficult to navigate “against the grain”.
    • Run: The “run” factor of a Maze is how long straightaways tend to go before forced turnings present themselves. A Maze with a low run won’t have straight passages for more than three or four cells, and will look very random. A Maze with a high run will have long passages going across a good percentage of the Maze, and will look similar to a microchip.
    • Elite: The “elitism” factor of a Maze indicates the length of the solution with respect to the size of the Maze. An elitist Maze generally has a short direct solution, while a non-elitist Maze has the solution wander throughout a good portion of the Maze’s area. A well designed elitist Maze can be much harder than a non-elitist one.
    • Symmetric: A symmetric Maze has symmetric passages, e.g. rotationally symmetric about the middle, or reflected across the horizontal or vertical axis. A Maze may be partially or totally symmetric, and may repeat a pattern any number of times.
    • River: The “river” characteristic means that when creating the Maze, the algorithm will look for and clear out nearby cells (or walls) to the current one being created, i.e. it will flow (hence the term “river”) into uncreated portions of the Maze like water. A perfect Maze with less “river” will tend to have many short dead ends, while a Maze with more river will have fewer but longer dead ends.

    Focus: The focus class is obscure, but shows that Maze creation can be divided into two general types: Wall adders, and passage carvers. This is more of an algorithmic difference when generating, as opposed to a visual difference when observing, but is still useful to consider. The same Maze can be often generated in both ways:

    • Wall adders: Algorithms that focus on walls start with an empty area (or an outer boundary) and add walls. In real life, a life size Maze composed of hedges, tarps, or wood walls, is a definite wall adder.
    • Passage carvers: Algorithms that focus on passages start with a solid block and carve passages. In real life, a Maze composed of mine tunnels, or running in the inside of pipes, is a passage carver.
    • Template: Mazes can of course be both passage carved and wall added, and some computer algorithms do just that. A Maze template refers to a general graphic that isn’t a Maze, which is then modified to be a valid Maze in as few steps as possible, but still has the texture of the original graphic template. Complicated Maze styles like interlocking spirals are easier to do on a computer as templates, as opposed to trying to create a valid Maze while keeping it conforming to whatever style at the same time.

    Other: The above is by no means a comprehensive list of all possible classes or items within each class. They’re just the types of Mazes I’ve actually created. 🙂 Note most every type of Maze, including Mazes with special rules, can be expressed as a directed graph, where you have a finite number of states and a finite number of choices at each state, which is called Maze equivalence. Here are some other classes and types of Mazes:

    • Direction: This is where certain passages can only be traveled in one way. In Computer Science terms, such a Maze would be described by a directed graph, as opposed to an undirected graph like all the others.
    • Segmented: This is where a Maze has different sections of its area falling in different classes.
    • Infinite length Mazes: It’s possible to create an infinitely long Maze (a finite number of columns by as many rows as you like) by only keeping part of the Maze in memory at a time and “scrolling” from one end to the other, discarding earlier rows while creating later rows. One way is with a modified version of the Hunt and Kill algorithm. Visualize the potentially infinitely long Maze as a long film reel, composed of individual picture frames, where just two consecutive frames are kept in memory at a time. Run the Hunt and Kill algorithm, however give bias to the top frame so it gets finished first. Once finished, it’s no longer needed, so can be printed out, etc. Either way, discard it, make the partially created bottom frame be the new top frame, and clear a new bottom frame. Repeat the process until you decide to stop, at which point let Hunt And Kill finish both frames. The only limitation is the Maze will never have a path that doubles back toward the entrance for a length greater than two frames. An easier way to make an infinite Maze is with Eller’s algorithm, as it already makes Mazes one row at time, so simply keep letting it add rows to the Maze forever.
    • Virtual fractal Mazes: A virtual Maze is one where the whole Maze isn’t stored in memory at once. For example only store the 100×100 section of passages or so nearest your location, in a simulation where you walk through a large Maze. An extension of nested fractal Mazes can be used to create virtual Mazes of enormous size, such as a billion by a billion passages. Note a life size version of a billion by billion Maze (with six feet between passages) would cover the Earth’s surface over 19000 times! Consider a 10^9 by 10^9 passage Maze, or a 10×10 Maze nested with 9 levels total. If we want at least a 100×100 section around us, we only need to create the 100×100 passage submaze at the lowest level, and the seven 10×10 Mazes it’s nested within, to know exactly where the walls lie within a 100×100 section. (Actually it’s best to have four adjacent 100×100 sections forming a square, in case you’re near the edge or corner of a section, but the same concept applies.) To ensure the Maze remains consistent and never changes as you move around, have a formula to determine a random number seed for each coordinate at each nesting level. Virtual fractal Mazes are similar to a Mandelbrot set fractal, where the pictures in a Mandelbrot exist virtually, where you just need to visit a particular coordinate at a high enough zoom level for them to reveal themselves.

    Maze Creation Algorithms

    Here’s a list of general algorithms to create the various classes of Mazes described above:

    • Perfect: Creating a standard perfect Maze usually involves “growing” the Maze while ensuring the no loops and no isolations restriction is kept. Start with the outer wall, and add a wall segment touching it at random. Keep on adding wall segments to the Maze at random, but ensure that each new segment touches an existing wall at one end, and has its other end in an unmade portion of the Maze. If you ever added a wall segment where both ends were separate from the rest of the Maze, that would create a detached wall with a loop around it, and if you ever added a segment such that both ends touch the Maze, that would create an inaccessible area. This is the wall adding method; a nearly identical way to do it is passage carved, where new passage sections are carved such that exactly one end touches an existing passage.
    • Braid: To create a Maze without dead ends, basically add wall segments throughout the Maze at random, but ensure that each new segment added will not cause a dead end to be made. I make them with four steps: (1) Start with the outer wall, (2) Loop through the Maze and add single wall segments touching each wall vertex to ensure there are no open rooms or small “pole” walls in the Maze, (3) Loop over all possible wall segments in random order, adding a wall there if it wouldn’t cause a dead end, (4) Either run the isolation remover utility at the end to make a legal Maze that has a solution, or be smarter in step three and make sure a wall is only added if it also wouldn’t cause an isolated section.
    • Unicursal: One way to create a random unicursal Maze is to take a perfect Maze, seal off the exit so there’s only the one entrance, then add walls bisecting each passage. This will turn each dead end into a U-turn passageway, and there will be a unicursal passage starting and ending at the original Maze’s beginning, that will follow the same path as someone wall following the original Maze. The new unicursal Maze will have twice the dimensions of the original perfect Maze it was based on. Small tricks may be done to have the start and end not always be next to each other: When creating the perfect Maze, never add segments attached to the right or bottom walls, so the resulting Maze will have an easy solution that follows that wall. Have the entrance at the upper right, and after bisecting to create the unicursal routing, remove the right and bottom wall. This will result in a unicursal Maze that starts at the upper right and ends at the lower left.
    • 3D: Three and higher dimensional Mazes can be created just like the standard 2D perfect Maze, except from each cell you can move randomly to six instead of four other orthogonal cells. These Mazes are generally passage carved due to the extra dimensions.
    • Weave: Weave Mazes are basically done as passage carved perfect Mazes, except when carving a passage you’re not always blocked by an existing passage, as you have the option to go under it and still preserve the “perfect” quality. On a monochrome bitmap, a Weave Maze can be represented with four rows per passage (two rows per passage is enough for a standard perfect Maze) where you have one row for the passage itself and the other three rows to make it unambiguous when another nearby passage goes under instead of just having a dead end near the first passage. For aesthetics you may want to look ahead before carving under an existing passage, to ensure you can continue to carve once you’re completely under it, so there won’t be any dead ends that terminate under a passage. Also, after carving under a passage, you may want to invert the pixels adjacent to the intersection, making it so newer passages can go over instead of always under existing ones.
    • Crack: Crack Mazes are basically done as wall added perfect Mazes, except there are no distinct tessellation cells other than random pixel locations. Pick a pixel that’s already set as a wall, pick another random location, and “shoot” or start drawing a wall toward the second location. However, make sure you stop just before running into any existing wall, so as not to create an isolation. Stop after you haven’t been able to add any significant walls in a while. Note that random locations to draw to that may be anywhere else in the Maze, will make it so there will be several straight lines going across the Maze, and other proportionally smaller walls as you look between them, the number of walls only being limited by the pixel resolution. This makes the Maze look very much like the surface of a leaf, so this is technically a fractal Maze.
    • Omega: Omega style Mazes involve defining some grid, defining how the cells link up with each other, and how to map the vertexes that surround each cell to the screen. For example, for the triangular Delta Maze with interlocking triangular cells: (1) There’s a grid where each row has a number of cells that increases by two. (2) Each cell is connected to the cells adjacent to it in that row, except the third passage is linked to an appropriate cell in the row above or below based on whether it’s in an odd or even column (i.e. whether the triangle is pointing up or down). (3) Each cell uses the math for a triangle to figure out where to draw it on the screen. You can draw all walls on the screen ahead of time and passage carve the Maze, or keep some modified array in memory and render the whole thing when complete.
    • Hypermaze: A hypermaze in a 3D environment is similar to the reverse of a standard 3D non-hypermaze, where blocks become open spaces and vice versa. While a standard 3D Maze consists of a tree of passages through a solid area, a hypermaze consists of a tree of bars or vines through an open area. To create a hypermaze, start with solid top and bottom faces, then grow tangled vines from these faces to fill the space between, to make it harder to pass a line segment between the two faces. As long as each vine connects with either the top or bottom, the hypermaze will have at most a single solution. As long as no vine connects with both the top and bottom (which would form an impassable column), and as long as there are no vine loops in the top and bottom sections that cause them to be inextricably linked with each other like a chain, the hypermaze will be solvable.
    • Planair: Planair Mazes with unusual topology are generally done as an array of one or more smaller Mazes or Maze sections, where it’s defined how the edges connect with each other. A Maze on the surface of a cube is just six square Maze sections, where when the part being created runs into an edge it flows onto another section and onto the right edge appropriately.
    • Template: Mazes based on templates are done by simply starting with the base template image, then running the isolation remover to ensure the Maze has a solution, followed by the loop remover to ensure the Maze is hard enough, resulting in a perfect Maze that still looks very similar to the original image. For example, to create a Maze composed of interlocking spirals, just create some random spirals without worrying whether it’s a Maze or not, then run it through the isolation and loop removers.

    Perfect Maze Creation Algorithms

    There are a number of ways of creating perfect Mazes, each with its own characteristics. Here’s a list of specific algorithms. All of these describe creating the Maze by carving passages, however unless otherwise specified each can also be done by adding walls:

    • Recursive backtracker: This is somewhat related to the recursive backtracker solving method described below, and requires stack up to the size of the Maze. When carving, be as greedy as possible, and always carve into an unmade section if one is next to the current cell. Each time you move to a new cell, push the former cell on the stack. If there are no unmade cells next to the current position, pop the stack to the previous position. The Maze is done when you pop everything off the stack. This algorithm results in Mazes with about as high a “river” factor as possible, with fewer but longer dead ends, and usually a very long and twisty solution. It runs quite fast, although Prim’s algorithm is a bit faster. Recursive backtracking doesn’t work as a wall adder, because doing so tends to result in a solution path that follows the outside edge, where the entire interior of the Maze is attached to the boundary by a single stem.
    • Prim’s algorithm: This requires storage proportional to the size of the Maze. During creation, each cell is one of three types: (1) “In”: The cell is part of the Maze and has been carved into already, (2) “Frontier”: The cell is not part of the Maze and has not been carved into yet, but is next to a cell that’s already “in”, and (3) “Out”: The cell is not part of the Maze yet, and none of its neighbors are “in” either. Start by picking a cell, making it “in”, and setting all its neighbors to “frontier”. Proceed by picking a “frontier” cell at random, and carving into it from one of its neighbor cells that are “in”. Change that “frontier” cell to “in”, and update any of its neighbors that are “out” to “frontier”. The Maze is done when there are no more “frontier” cells left (which means there are no more “out” cells left either, so they’re all “in”). This algorithm results in Mazes with a very low “river” factor, with many short dead ends, and the solution is usually pretty direct as well. It also runs very fast when implemented right, with only Eller’s algorithm being faster.
    • Kruskal’s algorithm: This algorithm is interesting because it doesn’t “grow” the Maze like a tree, but rather carves passage segments all over the Maze at random, but yet still results in a perfect Maze in the end. It requires storage proportional to the size of the Maze, along with the ability to enumerate each edge or wall between cells in the Maze in random order (which usually means creating a list of all edges and shuffling it randomly). Label each cell with a unique id, then loop over all the edges in random order. For each edge, if the cells on either side of it have different id’s, then erase the wall, and set all the cells on one side to have the same id as those on the other. If the cells on either side of the wall already have the same id, then there already exists some path between those two cells, so the wall is left alone so as to not create a loop. This algorithm yields Mazes with a low “river” factor, but not as low as Prim’s algorithm. Merging the two sets on either side of the wall will be a slow operation if each cell just has a number and are merged by a loop. Merging as well as lookup can be done in near constant time by giving each cell a node in a tree structure, with the id at the root, where merging is done quickly by splicing the trees together. Done right, this algorithm runs reasonably fast, but not as fast as either of the above two, because of the edge list and set management.
    • Aldous-Broder algorithm: The interesting thing about this algorithm is it generates all possible Mazes of a given size with equal probability. It also requires no extra storage or stack. Pick a point, and move to a neighboring cell at random. If an uncarved cell is entered, carve into it from the previous cell. Keep moving to neighboring cells until all cells have been carved into. This algorithm yields Mazes with a low “river” factor, only slightly higher than Kruskal’s algorithm. (This means for a given size there are more Mazes with a low “river” factor than high “river”, since an average equal probability Maze has low “river”.) The bad thing about this algorithm is that it’s very slow, since it doesn’t do any intelligent hunting for the last cells, where in fact it’s not even guaranteed to terminate. However since the algorithm is simple it can move over many cells quickly, so finishes faster than one might think. On average it takes about seven times longer to run than the above algorithms, although in bad cases it can take much longer if the random number generator keeps making it avoid the last few cells. This can be done as a wall adder if the boundary wall is treated as a single vertex, i.e. if a move goes to the boundary wall, teleport to a random point along the boundary before moving again. As a wall adder this runs nearly twice as fast, because the boundary wall teleportation allows quicker access to distant parts of the Maze.
    • Wilson’s algorithm: This is an improved version of the Aldous-Broder algorithm, in that it produces Mazes exactly like that algorithm, with all possible Mazes generated with equal probability, except that Wilson’s algorithm runs much faster. It requires storage up to the size of the Maze. Begin by making a random starting cell part of the Maze. Proceed by picking a random cell not already part of the Maze, and doing a random walk until a cell is found which is already part of the Maze. Once the already created part of the Maze is hit, go back to the random cell that was picked, and carve along the path that was taken, adding those cells to the Maze. More specifically, when retracing the path, at each cell carve along the direction that the random walk most recently took when it left that cell. That avoids adding loops along the retraced path, resulting in a single long passage being appended to the Maze. The Maze is done when all cells have been appended to the Maze. This has similar performance issues as Aldous-Broder, where it may take a long time for the first random path to find the starting cell, however once a few paths are in place, the rest of the Maze gets carved quickly. On average this runs five times faster than Aldous-Broder, and takes less than twice as long as the top algorithms. Note this runs twice as fast when implemented as a wall adder, because the whole boundary wall starts as part of the Maze, so the first walls are connected much quicker.
    • Hunt and kill algorithm: This algorithm is nice because it requires no extra storage or stack, and is therefore suited to creating the largest Mazes or Mazes on the most limited systems, since there are no issues of running out of memory. Since there are no rules that must be followed all the time, it’s also the easiest to modify and to get to create Mazes of different textures. It’s most similar to the recursive backtracker, except when there’s no unmade cell next to the current position, you enter “hunting” mode, and systematically scan over the Maze until an unmade cell is found next to an already carved into cell, at which point you start carving again at that new location. The Maze is done when all cells have been scanned over once in “hunt” mode. This algorithm tends to make Mazes with a high “river” factor, but not as high as the recursive backtracker. You can make this generate Mazes with a lower river factor by choosing to enter “hunt” mode more often. It runs slower due to the time spent hunting for the last cells, but isn’t much slower than Kruskal’s algorithm. This can be done as a wall adder if you randomly teleport on occasion, to avoid the issues the recursive backtracker has.
    • Growing tree algorithm: This is a general algorithm, capable of creating Mazes of different textures. It requires storage up to the size of the Maze. Each time you carve a cell, add that cell to a list. Proceed by picking a cell from the list, and carving into an unmade cell next to it. If there are no unmade cells next to the current cell, remove the current cell from the list. The Maze is done when the list becomes empty. The interesting part that allows many possible textures is how you pick a cell from the list. For example, if you always pick the most recent cell added to it, this algorithm turns into the recursive backtracker. If you always pick cells at random, this will behave similarly but not exactly to Prim’s algorithm. If you always pick the oldest cells added to the list, this will create Mazes with about as low a “river” factor as possible, even lower than Prim’s algorithm. If you usually pick the most recent cell, but occasionally pick a random cell, the Maze will have a high “river” factor but a short direct solution. If you randomly pick among the most recent cells, the Maze will have a low “river” factor but a long windy solution.
    • Eller’s algorithm: This algorithm is special because it’s not only faster than all the others that don’t have obvious biases or blemishes, but its creation is also the most memory efficient. It doesn’t even require the whole Maze to be in memory, only using storage proportional to the size of a row. It creates the Maze one row at a time, where once a row has been generated, the algorithm no longer looks at it. Each cell in a row is contained in a set, where two cells are in the same set if there’s a path between them through the part of the Maze that’s been made so far. This information allows passages to be carved in the current row without creating loops or isolations. This is actually quite similar to Kruskal’s algorithm, just this completes one row at a time, while Kruskal’s looks over the whole Maze. Creating a row consists of two parts: Randomly connecting adjacent cells within a row, i.e. carving horizontal passages, then randomly connecting cells between the current row and the next row, i.e. carving vertical passages. When carving horizontal passages, don’t connect cells already in the same set (as that would create a loop), and when carving vertical passages, you must connect a cell if it’s a set of size one (as abandoning it would create an isolation). When carving horizontal passages, when connecting cells union the sets they’re in (since there’s now a path between them), and when carving vertical passages, when not connecting a cell put it in a set by itself (since it’s now disconnected from the rest of the Maze). Creation starts with each cell in its own set before connecting cells within the first row, and creation ends after connecting cells within the last row, with a special final rule that every cell must be in the same set by the time we’re done to prevent isolations. (The last row is done by connecting each pair of adjacent cells if not already in the same set.) One issue with this algorithm is that it’s not balanced with respect to how it treats the different edges of the Maze, where connecting vs. not connecting cells need to be done in the right proportions to prevent texture blemishes.
    • Recursive division: This algorithm is somewhat similar to recursive backtracking, since they’re both stack based, except this focuses on walls instead of passages. Start by making a random horizontal or vertical wall crossing the available area in a random row or column, with an opening randomly placed along it. Then recursively repeat the process on the two subareas generated by the dividing wall. For best results, give bias to choosing horizontal or vertical based on the proportions of the area, e.g. an area twice as wide as it is high should be divided by a vertical wall more often. This is the fastest algorithm without directional biases, although it has the obvious blemish of long walls crossing the interior. This algorithm is a form of nested fractal Mazes, except instead of always making fixed cell size Mazes with Mazes of the same size within each cell, it divides the given area randomly into a random sized 1×2 or 2×1 Maze. Recursive division doesn’t work as a passage carver, because doing so results in an obvious solution path that either follows the outside edge or else directly crosses the interior.
    • Binary tree Mazes: This is basically the simplest and fastest algorithm possible, however Mazes produced by it have a very biased texture. For each cell carve a passage either leading up or leading left, but not both. In the wall added version, for each vertex add a wall segment leading down or right, but not both. Each cell is independent of every other cell, where you don’t have to refer to the state of any other cells when creating it. Hence this is a true memoryless Maze generation algorithm, with no limit to the size of Maze you can create. This is basically a computer science binary tree, if you consider the upper left corner the root, where each node or cell has one unique parent which is the cell above or to the left of it. Binary tree Mazes are different than standard perfect Mazes, since about half the cell types can never exist in them. For example there will never be a crossroads, and all dead ends have passages pointing up or left, and never down or right. The Maze tends to have passages leading diagonally from upper left to lower right, where the Maze is much easier to navigate from lower right to upper left. You will always be able to travel up or left, but never both, so you can always deterministically travel diagonally up and to the left without hitting any barriers. Traveling down and to the right is when you’ll encounter choices and dead ends. Note if you flip a binary tree Maze upside down and treat passages as walls and vice versa, the result is basically another binary tree.
    • Sidewinder Mazes: This simple algorithm is very similar to the binary tree algorithm, and only slightly more complicated. The Maze is generated one row at a time: For each cell randomly decide whether to carve a passage leading right. If a passage is not carved, then consider the horizontal passage just completed, formed by the current cell and any cells to the left that carved passages leading to it. Randomly pick one cell along this passage, and carve a passage leading up from it (which must be the current cell if the adjacent cell didn’t carve). While a binary tree Maze always goes up from the leftmost cell of a horizontal passage, a sidewinder Maze goes up from a random cell. While binary tree has the top and left edges of the Maze one long passage, a sidewinder Maze has just the top edge one long passage. Like binary tree, a sidewinder Maze can be solved deterministically without error from bottom to top, because at each row, there will always be exactly one passage leading up. A solution to a sidewinder Maze will never double back on itself or visit a row more than once, although it will “wind from side to side”. The only cell type that can’t exist in a sidewinder Maze is a dead end with the passage facing down, because that would contradict the fact that every passage going up leads back to the start. A sidewinder Maze tends to have an elitist solution, where the right path is very direct, but there are many long false paths leading down from the top next to it.
    Algorithm Dead End % Type Focus Bias Free? Memory Time Solution %
    Unicursal 0 Tree Wall Yes N^2 261 100.0
    Recursive Backtracker 10 Tree Passage Yes N^2 24 19.0
    Hunt and Kill 11 (21) Tree Passage no 0 55 (105) 9.5 (3.9)
    Recursive Division 23 Tree Wall Yes N 8 7.2
    Binary Tree 25 Set Either no 0* 7 2.0
    Sidewinder 27 Set Either no 0* 8 2.6
    Eller’s Algorithm 28 Set Either no N* 10 4.2 (3.2)
    Wilson’s Algorithm 29 Tree Either Yes N^2 51 (26) 4.5
    Aldous-Broder Algorithm 29 Tree Either Yes 0 222 (160) 4.5
    Kruskal’s Algorithm 30 Set Either Yes N^2 32 4.1
    Prim’s Algorithm 36 (31) Tree Either Yes N^2 21 2.3
    Growing Tree 49 (39) Tree Either Yes N^2 43 11.0

    This table summarizes the characteristics of the perfect Maze creation algorithms above. The Unicursal Maze algorithm (unicursal Mazes are technically perfect) is included for comparison. Descriptions of the columns follow:

    • Dead End: This is the approximate percentage of cells that are dead ends in a Maze created with this algorithm, when applied to an orthogonal 2D Maze. The algorithms in the table are sorted by this field. Usually creating by adding walls is the same as carving passages, however if significantly different the wall adding percentage is in parentheses. The Growing Tree value can actually range from 10% (always pick newest cell) to 49% (always swap with oldest cell). With a high enough run factor the Recursive Backtracker can get lower than 1%. The highest possible dead end percentage in an 2D orthogonal perfect Maze is 66%, which would be a unicursal passage with a bunch of one unit long dead ends off either side of it.
    • Type: There are two types of perfect Maze creation algorithms: A tree based algorithm grows the Maze like a tree, always adding onto what is already present, having a valid perfect Maze at every step. A set based algorithm builds where it pleases, keeping track of which parts of the Maze are connected with each other, to ensure it’s able to link everything up to form a valid Maze by the time it’s done.
    • Focus: Most algorithms can be implemented by either carving passages or adding walls. A few can only be done as one or the other. Unicursal Mazes are always wall added since they involve bisecting passages with walls, although the base Maze can be created either way. Recursive Backtracker can’t be done as a wall adder because doing so tends to result in a solution path that follows the outside edge, where the entire interior of the Maze is attached to the boundary by a single stem. Similarly Recursive Division can only be done as a wall adder due to its bisection behavior. Hunt and Kill is technically only passage carved for a similar reason, although it can be wall added if effort is made to grow inward from all boundary walls equally.
    • Bias Free: This is whether the algorithm treats all directions and sides of the Maze equally, where analysis of the Maze afterward can’t reveal any bias. Binary Tree is extremely biased, where it’s easy traveling toward one corner and hard to its opposite. Sidewinder is also biased, where it’s easy traveling toward one edge and hard to its opposite. Eller’s algorithm tends to have a passage roughly paralleling the starting or finishing edges. Hunt and Kill is nearly bias free, although the back and forth systematic searching will give a slight bias along that axis.
    • Memory: This is how much extra memory or stack is required to implement the algorithm. Efficient algorithms only require and look at the Maze bitmap itself, while others require storage proportional to a single row (N), or proportional to the number of cells (N^2). Some algorithms don’t even need to have the entire Maze in memory (these are marked with a asterisk). Eller’s algorithm requires storage for a row, but more than makes up for that since it only needs to store the current row of the Maze in memory. Sidewinder also only needs to store one row of the Maze, while Binary Tree only needs to keep track of the current cell. Recursive Division requires stack up to the size of a row, but other than that doesn’t need to look at the Maze bitmap any.
    • Time: This gives an idea of how long it takes to create a Maze using this algorithm, lower numbers being faster. The numbers are only relative to each other (with the fastest standard algorithm being assigned speed 10) as opposed to in some units, because the time is dependent on the size of the Maze and speed of the computer. These numbers are from creating 100×100 passage Mazes in the latest version of Daedalus. Usually creating by adding walls is the same speed as carving passages, however if significantly different the wall adding time is in parentheses.
    • Solution: This is the percentage of cells in the Maze that the solution path passes through, for a typical Maze created by the algorithm. This assumes the Maze is 100×100 passages with the start and end in opposite corners. This is a measure of the “windiness” of the solution path. Unicursal Mazes have maximum windiness, since the solution goes throughout the entire Maze. Binary Tree has the minimum possible windiness, where the solution path simply crosses the Maze and never deviates away from or ceases to make progress toward the end. Usually creating by adding walls has the same properties as carving passages, however if significantly different the wall adding percentage is in parentheses.

    Maze Solving Algorithms

    There are a number of ways of solving Mazes, each with its own characteristics. Here’s a list of specific algorithms:

    • Dead end filler: This is a simple Maze solving algorithm. It focuses on the Maze, is always very fast, and uses no extra memory. Just scan the Maze, and fill in each dead end, filling in the passage backwards from the block until you reach a junction. This includes filling in passages that become parts of dead ends once other dead ends are removed. At the end only the solution will remain, or solutions if there are more than one. This will always find the one unique solution for perfect Mazes, but won’t do much in heavily braid Mazes, and in fact won’t do anything useful at all for those Mazes without dead ends.
    • Wall follower: This is another simple Maze solving algorithm. It focuses on you, is always very fast, and uses no extra memory. Start following passages, and whenever you reach a junction always turn right (or left). Equivalent to a human solving a Maze by putting their hand on the right (or left) wall and leaving it there as they walk through. If you like you can mark what cells you’ve visited, and what cells you’ve visited twice, where at the end you can retrace the solution by following those cells visited once. This method won’t necessarily find the shortest solution, and it doesn’t work at all when the goal is in the center of the Maze and there’s a closed circuit surrounding it, as you’ll go around the center and eventually find yourself back at the beginning. Wall following can be done in a deterministic way in a 3D Maze by projecting the 3D passages onto the 2D plane, e.g. by pretending up passages actually lead northwest and down lead southeast, and then applying normal wall following rules.
    • Cul-de-sac filler: This method finds and fills in cul-de-sacs or nooses, i.e. constructs in a Maze consisting of a blind alley stem that has a single loop at the end. Like the dead end filler, it focuses on the Maze, is always fast, and uses no extra memory. Scan the Maze, and for each noose junction (a noose junction being one where two of the passages leading from it connect with each other with no other junctions along the way) add a wall to convert the entire noose to a long dead end. Afterwards run the dead end filler. Mazes can have nooses hanging off other constructs that will become nooses once the first one is removed, so the whole process can be repeated until nothing happens during a scan. This doesn’t do much in complicated heavily braid Mazes, but will be able to invalidate more than just the dead end filler.
    • Blind alley filler: This method finds all possible solutions, regardless of how long or short they may be. It does so by filling in all blind alleys, where a blind alley is a passage where if you walk down it in one direction, you will have to backtrack through that passage in the other direction in order to reach the goal. All dead ends are blind alleys, and all nooses as described in the cul-de-sac filler are as well, along with any sized section of passages connected to the rest of the Maze by only a single stem. This algorithm focuses on the Maze, uses no extra memory, but unfortunately is rather slow. For each junction, send a wall following robot down each passage from it, and see if the robot sent down a path comes back from the same path (as opposed to returning from a different direction, or it exiting the Maze). If it does, then that passage and everything down it can’t be on any solution path, so seal that passage off and fill in everything behind it. This algorithm will fill in everything the cul-de-sac filler will and then some, however the collision solver will fill in everything this algorithm will and then some.
    • Blind alley sealer: This is like the blind alley filler, in that it also finds all possible solutions by removing blind alleys from the Maze. However this just fills in the stem passage of each blind alley, and doesn’t touch any collection of passages at the end of it. As a result this will create inaccessible passage sections for cul-de-sacs or any blind alley more complicated than a dead end. This algorithm focuses on the Maze, runs much faster than the blind alley filler, although it requires extra memory. Assign each connected section of walls to a unique set. To do this, for each wall section not already in a set, flood across the top of the walls at that point, and assign all reachable walls to a new set. After all walls are in sets, then for each passage section, if the walls on either side of it are in the same set, then seal off that passage. Such a passage must be a blind alley, since the walls on either side of it link up with each other, forming a pen. Note a similar technique can be used to help solve hypermazes, by sealing off space between branches that connect with each other.
    • Pledge algorithm: This is a modified version of wall following that’s able to jump between islands, to solve Mazes wall following can’t. It’s a guaranteed way to reach an exit on the outer edge of any 2D Maze from any point in the middle, however it’s not able to do the reverse, i.e. find a solution within the Maze. It’s great for implementation by a Maze escaping robot, since it can get out of any Maze without having to mark or remember the path in any way. Start by picking a direction, and always move in that direction when possible. When a wall is hit, start wall following until your chosen direction is available again. Note you should start wall following upon the far wall that’s hit, where if the passage turns a corner there, it can cause you to turn around in the middle of a passage and go back the way you came. When wall following, count the number of turns you make, e.g. a left turn is -1 and a right turn is 1. Only stop wall following and take your chosen direction when the total number of turns you’ve made is 0, i.e. if you’ve turned around 360 degrees or more, keep wall following until you untwist yourself. The counting ensures you’re eventually able to reach the far side of the island you’re currently on, and jump to the next island in your chosen direction, where you’ll keep on island hopping in that direction until you hit the boundary wall, at which point wall following takes you to the exit. Note Pledge algorithm may make you visit a passage or the start more than once, although subsequent times will always be with different turn totals. Without marking your path, the only way to know whether the Maze is unsolvable is if your turn total keeps increasing, although the turn total can get to large numbers in solvable Mazes in a spiral passage.
    • Chain algorithm: The Chain algorithm solves the Maze by effectively treating it as a number of smaller Mazes, like links in a chain, and solving them in sequence. You have to specify the start and desired end locations, and the algorithm will always find a path from start to end if one exists, where the solution tends to be a reasonably short if not the shortest solution. That means this can’t solve Mazes where you don’t know exactly where the end is. This is most similar to Pledge algorithm since it’s also essentially a wall follower with a way to jump between islands. Start by drawing a straight line (or at least a line that doesn’t double back on itself) from start to end, letting it cross walls if needed. Then just follow the line from start to end. If you bump into a wall, you can’t go through it, so you have to go around. Send two wall following “robots” in both directions along the wall you hit. If a robot runs into the guiding line again, and at a point which is closer to the exit, then stop, and follow that wall yourself until you get there too. Keep following the line and repeating the process until the end is reached. If both robots return to their original locations and directions, then farther points along the line are inaccessible, and the Maze is unsolvable.
    • Recursive backtracker: This will find a solution, but it won’t necessarily find the shortest solution. It focuses on you, is fast for all types of Mazes, and uses stack space up to the size of the Maze. Very simple: If you’re at a wall (or an area you’ve already plotted), return failure, else if you’re at the finish, return success, else recursively try moving in the four directions. Plot a line when you try a new direction, and erase a line when you return failure, and a single solution will be marked out when you hit success. When backtracking, it’s best to mark the space with a special visited value, so you don’t visit it again from a different direction. In Computer Science terms this is basically a depth first search. This method will always find a solution if one exists, but it won’t necessarily be the shortest solution.
    • Tremaux’s algorithm: This Maze solving method is designed to be able to be used by a human inside of the Maze. It’s similar to the recursive backtracker and will find a solution for all Mazes: As you walk down a passage, draw a line behind you to mark your path. When you hit a dead end turn around and go back the way you came. When you encounter a junction you haven’t visited before, pick a new passage at random. If you’re walking down a new passage and encounter a junction you have visited before, treat it like a dead end and go back the way you came. (That last step is the key which prevents you from going around in circles or missing passages in braid Mazes.) If walking down a passage you have visited before (i.e. marked once) and you encounter a junction, take any new passage if one is available, otherwise take an old passage (i.e. one you’ve marked once). All passages will either be empty, meaning you haven’t visited it yet, marked once, meaning you’ve gone down it exactly once, or marked twice, meaning you’ve gone down it and were forced to backtrack in the opposite direction. When you finally reach the solution, paths marked exactly once will indicate a direct way back to the start. If the Maze has no solution, you’ll find yourself back at the start with all passages marked twice.
    • Collision solver: Also called the “amoeba” solver, this method will find all shortest solutions. It focuses on you multiple times, is fast for all types of Mazes, and requires at least one copy of the Maze in memory in addition to using memory up to the size of the Maze. It basically floods the Maze with “water”, such that all distances from the start are filled in at the same time (a breadth first search in Computer Science terms) and whenever two “columns of water” approach a passage from both ends (indicating a loop) add a wall to the original Maze where they collide. Once all parts of the Maze have been “flooded”, fill in all the new dead ends, which can’t be on the shortest path, and repeat the process until no more collisions happen. (Picture amoebas surfing at the crest of each “wave” as it flows down the passages, where when waves collide, the amoebas head-butt and get knocked out, and form there a new wall of unconscious amoebas, hence the name.)
    • Shortest path finder: As the name indicates, this algorithm finds the shortest solution, picking one if there are multiple shortest solutions. It focuses on you multiple times, is fast for all types of Mazes, and requires quite a bit of extra memory proportional to the size of the Maze. Like the collision solver, this basically floods the Maze with “water”, such that all distances from the start are filled in at the same time (a breadth first search in Computer Science terms) however each “drop” or pixel remembers which pixel it was filled in by. Once the solution is hit by a “drop”, trace backwards from it to the beginning and that’s a shortest path. This algorithm works well given any input, because unlike most of the others, this doesn’t require the Maze to have any one pixel wide passages that can be followed. Note this is basically the A* path finding algorithm without a heuristic so all movement is given equal weight.
    • Shortest paths finder: This is very similar to the shortest path finder above, except this finds all shortest solutions. Like the shortest path finder, this focuses on you multiple times, is fast for all types of Mazes, requires extra memory proportional to the size of the Maze, and works well given any input since it doesn’t require the Maze to have any one pixel wide passages that can be followed. Also like the shortest path finder, this does a breadth first search flooding the Maze with “water” such that all distances from the start are filled in at the same time, except here each pixel remembers how far it is from the beginning. Once the end is reached, do another breadth first search starting from the end, however only allow pixels to be included which are one distance unit less than the current pixel. The included pixels precisely mark all the shortest solutions, as blind alleys and non-shortest paths will jump in pixel distances or have them increase.
    • Random mouse: For contrast, here’s an inefficient Maze solving method, which is basically to move randomly, i.e. move in one direction and follow that passage through any turnings until you reach the next junction. Don’t do any 180 degree turns unless you have to. This simulates a human randomly roaming the Maze without any memory of where they’ve been. It’s slow and isn’t guaranteed to ever terminate or solve the Maze, and once the end is reached it will be just as hard to retrace your steps, but it’s definitely simple and doesn’t require any extra memory to implement.
    Algorithm Solutions Guarantee? Focus Human Doable? Passage Free? Memory Free? Fast?
    Random Mouse 1 no You Inside / Above no Yes no
    Wall Follower 1 no You Inside / Above Yes Yes Yes
    Pledge Algorithm 1 no You Inside / Above Yes Yes Yes
    Chain Algorithm 1 Yes You + no Yes no Yes
    Recursive Backtracker 1 Yes You no Yes no Yes
    Tremaux’s Algorithm 1 Yes You Inside / Above no no Yes
    Dead End Filler All + no Maze Above no Yes Yes
    Cul-de-sac Filler All + no Maze Above no Yes Yes
    Blind Alley Sealer All + Yes Maze no no no Yes
    Blind Alley Filler All Yes Maze Above no Yes no
    Collision Solver All Shortest Yes You + no no no Yes
    Shortest Paths Finder All Shortest Yes You + no Yes no Yes
    Shortest Path Finder 1 Shortest Yes You + no Yes no Yes

    This table summarizes the characteristics of the Maze solving algorithms above. Maze solving algorithms can be classified and judged by these criteria. Descriptions of the columns follow:

    • Solutions: This describes the solutions the algorithm finds, and what the algorithm does when there’s more than one. An algorithm can pick one solution, or leave multiple solutions. Also the solution(s) can be any path, or they can be the shortest path. The dead end and cul-de-sac fillers (and the blind alley sealer when considering its inaccessible sections) leave all solutions, however they may also leave passages that aren’t on any solution path, so are marked “All +” above.
    • Guarantee: This is whether the algorithm is guaranteed to find at least one solution. Random mouse is “no” because it isn’t guaranteed to terminate, and wall follower and Pledge algorithm are “no” because they will fail to find a solution if the goal is within an island. The dead end and cul-de-sac fillers are “no” because they may not do anything to the Maze at all in purely braid Mazes.
    • Focus: There are two general types of algorithms to solve a Maze: Focus on “you”, or focus on the Maze. In a you-focuser, you have a single point (“You” above) or a set of points (“You +” above) and try to move them through the Maze from start to finish. In a Maze-focuser, you look at the Maze as a whole and invalidate useless passages.
    • Human Doable: This refers to whether a person could readily use the algorithm to solve the Maze, either while inside a life sized version, or while looking at a map from above. Some you-focuser algorithms can be implemented by a person inside (or above) the Maze, while some Maze-focusers can be implemented by a person, but only from above. Other algorithms are complicated or intricate enough they can only reliably be done by a computer.
    • Passage Free: This is whether the algorithm can be done anywhere. Some algorithms require the Maze to have obvious passages, or distinct edges between distinct vertices in graph terms, or one pixel wide passages when implemented on a computer. The wall follower, Pledge algorithm, and chain algorithm only require a wall on one side of you. The recursive backtracker and the shortest path(s) finders make their own paths through open spaces.
    • Memory Free: This is whether no extra memory or stack is required to implement the algorithm. Efficient algorithms only require and look at the Maze bitmap itself, and don’t need to add markers to the Maze during the solving process.
    • Fast: This is whether the solving process is considered fast. The most efficient algorithms only need to look at each cell in the Maze once, or can skip sections altogether. Running time should be proportional to the size of the Maze, or in Computer Science terms O(n^2) where n is the number of cells along one side. Random mouse is slow because it isn’t guaranteed to terminate, while the blind alley filler potentially solves the Maze from each junction.

    Other Maze Operations

    There are more things that can be done with Mazes beyond just creating and solving them, as described below:

    • Flood fill: A quick and dirty yet useful utility can be implemented with a single call to a graphics library’s Fill or FloodFill routine. FloodFill the passage at the beginning, and if the end isn’t filled, the Maze has no solution. For Mazes with an entrance and exit on the edges, FloodFill one wall, and the remaining edge marks out the solution. For Mazes with the start or goal inside the Maze, FloodFill the surrounding wall, and if the exit wall isn’t erased, wall following won’t work to solve it. Many Maze creation methods, solving methods, and other utilities involve “flooding” the Maze at certain points.
    • Isolation remover: This means to edit the Maze such that there are no passage sections that are inaccessible from the rest of the Maze, by removing walls to connect such sections to the rest of the Maze. Start with a copy of the Maze, then flood the passage at the beginning. Scan the Maze (preferably in a random order that still hits every possible cell) for any unfilled cells adjacent to a filled cell. Remove a wall segment in the original Maze at that point, flood the Maze at this new point, and repeat until every section is filled. This utility is used in the creation of braid and template Mazes.
    • Loop remover: This means to edit the Maze such that there are no loops or detached walls within it, every section of the Maze reachable from any other by at most one path. The way to do this is almost identical to the isolation remover, just treat walls as passages and vice versa. Start with a copy of the Maze, then flood across the top of the outer walls. Scan the Maze (preferably in a random other that still hits every possible wall vertex) for any unfilled walls adjacent to a filled wall. Add a wall segment to the original Maze at that point connecting the two wall sections, flood the Maze at this new point, and repeat until every section is filled. This utility is used in the creation of template Mazes, and can be used to convert a braid Maze to a perfect Maze that still looks similar to the original.
    • Bottleneck finder: This means to find those passages or intersection points in a Maze such that every solution to that Maze passes through them. To do this, run the left hand wall follower to get the leftmost solution, and run the right hand wall follower to get the rightmost solution, where places the two solutions have in common are the bottlenecks. That technique however only works for Mazes that wall following will successfully solve. For other Mazes, to find bottleneck passages, find any solution to the Maze, and also run the blind alley sealer (which may make the Maze unsolvable if it treats an entrance or exit within the Maze as a large blind alley). Parts of the solution path that go through sealed off passages, are bottlenecks.

    Algorithm Implementations

    • Daedalus: All the Maze creation and solving algorithms described above are implemented in Daedalus, a free Windows program available for download. Daedalus comes with its complete source code, which can be viewed to see more information about and specific implementations of these algorithms.

    Back to Think Labyrinth!


    This site produced by Walter D. Pullen (see Astrolog homepage), hosted on Magitech and astrolog.org, created using Microsoft FrontPage, page last updated March 3, 2009.

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    3. Team Of Monkeys – some very cool mazes, for free and larger sizes and vectors files for sale as clipart. – http://www.teamofmonkeys.com/
    4. Maze of Mazes – Collection of image mazes. – http://mazeofmazes.net63.net
    5. Handy Dandy Maze Editor – http://www.berighteous.com/euphoria/mazed.zip
    6. Experience Mazes, REALLY! – http://www.abcfamilyadventures.co.uk/experience/mazes
    7. Maze Master – Funky Mazes – http://www.mazemaster.com/MazeMaster/img/books/mm-ult002.jpg
    8. Ink Blot Mazes – Same artist as Team Of Monkeys, but  a much tidier site and also with some quotes and other puzzles – http://www.inkblotmazes.com/
    9. Maze Algorithms – Think Labyrinth – http://www.astrolog.org/labyrnth/algrithm.htm
    10. Mazes on Facebook – an public album on facebook of mazes. COOL! – http://www.facebook.com/album.php?aid=16542&id=678580452&l=76507ed7ba

    **********************

    ****************

    Surface Mazes

    I also enjoy creating mazes. Recently I’ve been focusing on creating mazes on the surfaces of various geometric shapes (or, more accurately, I’ve been focusing on creating computer programs which generate random mazes of the surfaces of geometric shapes). Pictured to the right is a maze on the surface of a “buckyball” (i.e. a truncated icosahedron, or soccer ball).

    The maze is “perfectly formed”, meaning that there are no loops, and every spot on the maze is reachable from every other spot on the maze. This is really just a prototype; I plan to make a nicer one with a solid wood structure beneath the laminated paper surface. The pictured one is simply heavy paper laminated with clear contact paper and taped at the edges of tha faces. The laminate allows one to use an erasable marker on the surface when solving.

    I created a maze on the surface of a cube for my first Puzzle Party back in fall of 2004. I did not have one at EPP2, but I expect similar puzzles to crop up again at future Parties.

    ***********

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    Mazes for Discussion

    Adapted from Business Mazes by Joni Farthing, Hart-Davis, 1981

    maze

    What is a maze?

    A maze is a puzzling game. A garden maze is a network, or labyrinth, of paths between high hedges. The puzzle is to find the paths that will lead most quickly to the exit, but the hedges prevent you from seeing where alternative routes lead.

    How to read a maze

    There are five mazes designed to introduce and practise language common in business situations. Just like the garden maze, each one involves making decisions. However, the aim is not to reach the exit as quickly as possible, but to solve the problem effectively.

    The entrance is ‘the situation’. Everyone starts here, and then chooses a course of action from 1. If none of the alternatives are exactly the path you would like to take, choose the one nearest to the ideal. Each decision leads to another number in the maze, which shows how the situation has changed because of the action you have taken. Write down every number you turn to. This is your numbers-route, (If you find yourself on a familiar path, think again!) Continue until the end, or exit, of the maze is reached.

    In a garden maze you cannot use a ladder to take a quick look over the hedge to see where other paths lead. In this book, you should not look at routes unless they are indicated by your decisions.

    I suggest that you work through the maze in a group, but you can do it by yourself, discussing each choice in detail before reaching a joint decision and going to the next stage. Practise your English by trying to convince others that your point of view is right, but listen to their opinions too. Keep a record of the problems and your decisions. After you finish the maze you can either discuss it further or go back along your number-route and take another look at the unfamiliar words and expressions you met on your way. Write a report when you have finished.

    No Smoking

    The Salesman

    The Complaint

    The Reference

    Reg Collins

    El Maze de Politico

    March 18, 2009
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    They that mistake life’s accessories for life itself are like them that go too fast in a maze: their very haste confuses them

    Seneca quotes (Roman philosopher, mid-1st century AD)

    Maze of Monkey Illusion – 2009
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    James Moreland: Well, actually it’s mostly students I’m experimenting on now.

    Kurt Godel: My God, the mazes must be enormous.


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    It is easier to penetrate your audience with one sharp, clean point or idea, thand with a maze of half-baked unremarkable, uninspiring ideas that will never motivate or be remembered.

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    Maze Museum 2006
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    Happiness, that grand mistress of the ceremonies in the dance of life, impels us through all its mazes and meanderings, but leads none of us by the same route.

    Charles Caleb Colton quotes (English sportsman and writer, 1780-1832)


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    Rupert Murdoch rolls the dice at News Corp.

    March 14, 2009
    By PATRICK GOLDSTEIN
    March 14, 2009

    Like him or loathe him, Rupert Murdoch is the last of the great media swashbucklers, a throwback to the pirates, cutthroats and visionaries who used to run the business before it was engulfed and devoured by giant risk-averse corporate behemoths. The earthquake that rocked News Corp. this week was a typical Murdoch seismic event. As one of his top executives once told me: “Rupert is a gambler. He tolerates noble failure more than complacency.”

    More than anything else, that maxim seems to best explain the dramatic moves Murdoch made Thursday. Before his longtime No. 2 man Peter Chernin had finished cleaning out his desk, Murdoch boldly revamped his company’s executive superstructure. There were many moves in Rupert’s chess game, but the key ones were all about Murdoch’s lucrative but endangered profit center: the Fox TV business. He essentially has taken three executives who had great success propelling Fox film divisions and installed them in positions of power, running the TV wing of the empire.

    20th Century Fox Co-Chairmen Jim Gianopulos and Tom Rothman, who’ve presided over the most disciplined and profitable movie studio of the past decade, will now also oversee TV production along with a host of Chernin’s former duties, most crucially much of News Corp.’s new media ventures. This includes online media ventures such as Hulu that Chernin had practically willed into existence when most established media companies were still obsessed with suing YouTube and keeping their most valued programming off the Internet.

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    I’ve been tough on them over the past year, but giving Rothman and Gianopulos more clout was a no-brainer — they’ve earned it. Murdoch’s most unorthodox move is the promotion of Peter Rice, until now the head of the Fox Searchlight specialty film division, who will run the Fox TV network. Hugely successful as a specialty division czar, having made or acquired such hits as “Sideways,” “Napoleon Dynamite,” “Little Miss Sunshine,” “Juno” and this year’s Oscar winner, “Slumdog Millionaire,” Rice has always been Rupert’s fair-haired boy. For a man whose relationships with his own sons have blown hot and cold, with the offspring often chafing under their father’s rule, Rice has been the good, dutiful son, his relations with Rupert unburdened by blood relations.

    Very buttoned-down, always wary of the media spotlight, Rice plays his cards close to the vest. Even when he was having lunch with an old friend this week, he acted as if he was staying put, saying he felt most comfortable remaining at Searchlight. But Murdoch clearly wanted to give Rice a bigger portfolio. He’s quietly made himself an indispensable News Corp. player, careful enough not to seek credit for his triumphs, shrewd enough to avoid the blame for his rare missteps, such as Fox Atomic, the genre division that was a very quiet failure.

    Running Fox’s TV division, Rice will either succeed or fail in a very public way, since most Fox insiders see him as Chernin’s eventual successor as Rupert’s right-hand man. At 42, Rice is closer in age to Rupert’s sons and daughter (we’re not counting the toddlers Murdoch has from his most recent marriage), making him a generational choice as well, since he will surely someday be working alongside whichever one of the Murdoch offspring ends up inheriting the empire after their father’s death or retirement.

    So why put the future of the TV network, the empire’s most valuable resource, in the hands of a TV neophyte? Murdoch is a gambler, with a gambler’s instincts. As anyone in the media game will tell you, the network TV model is broken, on the brink of collapse, just as the newspaper business and the music industry before it. It is no longer time for incremental fixes; radical change is needed. That’s what Rice is there to provide. If you believe in upending the entire business, searching for a new economic model, you don’t hire a solid, experienced veteran, you hire an outsider who’s not tied to the old ways of thinking. In Murdoch’s announcement, he didn’t say Rice was the right person to “run” the TV business; he said he was the right person to “transform” it.

    Murdoch has looked at the TV business and seen the obvious: TV’s old mass audience is quickly migrating to YouTube, Hulu and Pirate Bay. The TV models that still work are niche businesses, cable channels that appeal to specific audiences, not the vast mainstream wasteland. The executive who Murdoch ousted Thursday was Peter Liguori, who’d done a great job reinventing Fox’s FX cable channel but couldn’t get any traction running the network. I suspect Rice will learn from Liguori’s experience. He will have to find a way to rethink and reinvent network TV, finding a way to free it from the old mass-audience model that — with rare exceptions such as Fox’s own “American Idol” — is going, going, gone.

    Seeing a new business with fresh eyes doesn’t guarantee success. But it doesn’t bode ill either. Chernin was a TV guy who started in the book business and ended up running Murdoch’s film studio, with pretty impressive results wherever he went. Barry Diller was a success untold times over, moving from TV to film and then back to TV — he’s the one who invented the Fox network in the first place. But Brandon Tartikoff, who was a genius at running a TV network, stumbled badly overseeing Paramount Pictures. Andy Lack, a savvy TV news guy, was a disaster running Sony Music. If NBC Universal’s Jeff Zucker could sing, he’d be crooning, “Regrets, I’ve had a few, mostly like hiring Ben Silverman to run the network.” It’s a crap shoot. But Rupert believes that talent is translatable. His operating instinct is to give new or bigger jobs to people who’ve shown a gift for consistently growing their businesses and keeping their divisions in the black.

    The last thing anyone has to worry about is Fox Searchlight. Even with Rice gone, it will be in good hands with its chief operating officers, marketing whiz Nancy Utley and distribution guru Steve Gilula, who are held in great regard, even by longtime rivals. Rice’s charisma may be missed, but it’s unlikely that Searchlight’s business model will change. It has been the one company that has consistently married art to commerce, finding quirky films that could cross over to a broader audience.

    Under Murdoch, News Corp. has been a strange hybrid of wildly different management styles and corporate cultures — intensely entrepreneurial, quick to embrace innovation, largely decentralized and always, but always, a realm that celebrates fierce competition.

    But for all of its survival-of-the-fittest ethos, for all its willingness to adapt to hard new realities, News Corp. is still the equivalent of a Middle Eastern dictatorship. With Chernin and now Rice, its executives have succeeded on merit. But the top job at the company is a Murdoch family reserve, which is why Chernin packed his bags in the first place. One of the kids will eventually be given the keys to the kingdom. Our fascination with all these dramatic changes revolves around how much of the kingdom will be left when Rupert finally passes the torch.

    ‘Twilight’ rumor is eclipsed

    I hate to be the skunk at the picnic, but Summit Entertainment has not — I repeat NOT — hired “Orphanage” director Juan Antonio Bayona to direct “Eclipse,” the third film in the wildly successful “Twilight” series.

    That would be the exact opposite of the “news” circulating earlier this week, which stated that Summit “has tapped Spanish director Juan Antonio Bayona to direct ‘Eclipse.’ ”

    By sheer coincidence, I had lunch Thursday with Erik Feig, who’s president of production at Summit and the man most involved with managing the hit series of films. (“New Moon,” the second film in the series, begins production later this month with Chris Weitz at the helm.)

    Feig was shocked to see the media reports saying Summit had hired Bayona.

    “The ‘Eclipse’ directing job hasn’t been offered to Juan Antonio or anyone else,” he told me. “We’ve met with three or four talented filmmakers and we’ll be meeting with three or four more other candidates before we make any decision. No one has been offered the job.”

    As it turns out, Bayona was in town and had a Wednesday meeting with Summit execs, who are certainly impressed by his résumé. Bayona has also met with “Twilight” author Stephenie Meyer, who has a lot to say about any key creative choices made on each film in the series. On the other hand, Bayona has told friends that he isn’t sure he wants to tackle the film. Though he also admires the series, he’s concerned about how much creative involvement he would have coming in to direct the third installment in a series, where most of the casting and character development is already in place.

    patrick.goldstein @latimes.com

    Mazes, Cartoons, Fun, fun and more fun.

    March 14, 2009

    Welcome to Team Of Monkeys . Com !


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    They that mistake life’s accessories for life itself are like them that go too fast in a maze: their very haste confuses them

    Seneca quotes (Roman philosopher, mid-1st century AD)

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    “Boris Podolsky: James! How’s the rat business?

    James Moreland: Well, actually it’s mostly students I’m experimenting on now.

    Kurt Godel: My God, the mazes must be enormous.


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    The man of character, sensitive to the meaning of what he is doing, will know how to discover the ethical paths in the maze of possible behavior.

    Earl Warren quotes (American Republican Politician and Judge, 18911974)



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    Portrait– 2009

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    Maze Portrait of Barak Obama – By Yonatan Frimer

    Real obstacles don’t take you in circles. They can be overcome. Invented ones are like a maze.
    Barbara Sher

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    Maze Zen Impossible – Yonatan Frimer 2009

    It is easier to penetrate your audience with one sharp, clean point or idea, thand with a maze of half-baked unremarkable, uninspiring ideas that will never motivate or be remembered.

    ~ Stavros Cosmopulos quotes

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    Happiness, that grand mistress of the ceremonies in the dance of life, impels us through all its mazes and meanderings, but leads none of us by the same route.

    Charles Caleb Colton quotes (English sportsman and writer, 1780-1832)


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    ~ Seneca quotes



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    The Team of Monkeys Pirate ship. Where is the rum?
    Pirates Monkeys Team Delta echo niner, by Yonatan Frimer and RSL

    Monkeyed Mission to the Moon 2005 Yonatan Frimer and RSL

    Portaits, mazes, news and more.

    March 12, 2009
    Osama        or       Obama
    terrorist osama bin ladenObama for President

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    First Lady for President – Hillary Clinton                          Mona Lisa Replica 2008
    Hillary ClintonMoni Yoni

    Nuclear Obama: Will Cap-and-Trade Plans Spur Nuclear Revival?

    Click here for original article

    Will President Obama—no huge booster of nuclear power on the campaign trail—become the nuclear industry’s best friend?

    ObamaChu_art_257_20090311151126.jpg

    Nuclear dream team? (AP)

    Here’s the thinking making the rounds in pro-nuclear circles: The Obama administration has talked up the need to dramatically curb greenhouse-gas emissions, and even included revenues from a non-existent cap-and-trade scheme in its 2010-2014 budget. To curb emissions so much will require an across-the-board development of low-emissions energy, from wind farms to, yes, more new nuclear plants.

    Nuclear advocate and author William Tucker makes the optimists’ case in the American Spectator (tip of the hat). When climate policies run into opposition from Congress, led by coal-dependent states, the nuclear lightbulb will turn on:

    Someone in the administration — probably Energy Secretary Steven Chu, who knows in his heart that wind and solar can’t cut it — will suggest that that a carbon tax be coupled with the revival of nuclear power. Suddenly, the dam will break. NRC regulatory mazes that are still trying to protect us from Three Mile Island will be swept aside. Construction schedules will be accelerated. (The TVA just built a new reactor at Watts Bar in three years and under budget, using a license granted in the 1970s.) Tens of thousands of construction jobs will be created overnight. The French and Japanese will provide the financing. We may even revive the steel industry in the process.

    The idea that the climate-change imperative will give fresh legs to nuclear power isn’t entirely new; that’s what’s pushing once-hostile environmentalists toward the pro-nuclear camp. And a carbon tax or at least expensive emissions in a cap-and-trade program would go a long way toward improving nuclear power’s currently grim economics.

    But even an Obama administration bear hug that “sweeps aside regulatory mazes” won’t necessarily “accelerate construction schedules”—those depend in large part on financing and getting a hold of sometimes limited nuclear components. And while a big nuclear build out would indeed create as many as 20,000 jobs, it would be hard to create them overnight, given the three-decade atrophy of the U.S. nuclear industry.

    What’s really missing is any discussion of nuclear waste. Now that Yucca Mountain’s been given the Old Yeller treatment, there is no long-term solution for storing nuclear waste that’s remotely close to fruition. For the current fleet of nuclear reactors, which produce about 2,000 tons of radioactive fuel a year, the death of Yucca Mountain just means business as usual.

    But sooner or later, if nuclear power becomes an even bigger part of the nation’s energy mix, the nuclear waste problem is going to have to become an even bigger part of the answer.

    Please enjoy these mazes.

    Maze Kong - 2006 Mazes

    I also do Technical Animations of Scientfic products
    Especially for advanced technology. For Example:

    Y_Frimer Maze in Chinese Newspaper, The Information Times

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    2006 Mazes by YFrimer April Showers Bring Maze FlowersMazell and other mazes 2006/7 yfrimerMy MAZErotti does 185, I got arrested now I don't drive - Joe Walsh


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    Maze of Mazes “Most Popular Mazes” Booklet PDF

    Maze Portraits:

    Michael Jackson         Keanue                                        Elvis
    Michael Jackson Maze portrait Keanu portrait maze maze The King of Rock - portrait by yonatan frimer

    Gwen Stefani                                         Bashar Al Assad                           Shimon Peres
    gwen stephani maze portrait portrait maze bashar assad shimon peres, president of israel, portrait by yonatan frimer

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    Arcadi Gaydamak                         George W. Bush                                    Bill Clinton
    Arcadi Gaydamak maze portrait portrait maze George W Bush Bill Clinton, former US president

    Amir Peretz                                         The Lubavitcher Rebbe
    portrait maze amir peretz the lubavitcher rebbe
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    I love making scientific animations,
    This one follows an electron thru
    a solar panel:


    The Mazeum – Ink On Paper, Winter 2006, by Y. Frimer
    Maze um - at least act snooty if this doesn't download


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    Check out more mazes on our new site:
    Maze of Mazes – Created by Yonatan Frimer
    The site basically is an album of some of my favorite mazes with the ability to download them in various formats and sizes

    OraGanizational  Overview

    Team of monkeys . com, founded in  February 1964* is a subsidiary of STOM Research, founded in December 1961*. Utilizing the vast resources at its disposal, STOM Research has resulted in conclusive evidence that monkeys working in teams can benefit the human race in ways not previously accepted because monkeys working alone are unable to perform the same task(s).

    Notable highlights from STOM Resarch’s 59 decades.

    • 1956  – Dr Otto Verbraucher wins science recognition accolades award 1956
    • 1959  – Able and Miss Baker – First team of monkeys to go to space and come back
    • 1962  – Cuban Missle Crisis forces STOM resEarch Labs in Las Tunas to close.
    • 1977  – Shakespear Theorum proved wrong. Even an infinite number o monkeys working in an organized team will still not render the complete works of shakespears complete works in proper order.
    • 1988 – Internet is opened to the commercial public enabling teamofmonkeys.com to be available to non-military personnel.

    Making sense of the foreclosure-rescue maze

    March 8, 2009

    The Obama administration’s release of details and guidelines for its $275 billion foreclosure rescue plan that could help as many as 9 million at-risk mortgage holders nationwide is step one in a process that will require patience, attention to detail, and a lot of cooperation on the parts of lenders and borrowers.

    What is not known is how many of those mortgage holders in New Hampshire and Maine will benefit from the two programs in the Make Home Affordable plan, which was crafted to help two different groups of struggling homeowners.

    Eligibile for help?

    To determine borrower eligibility for one of the two Making Home Affordable programs — Home Affordable Finance or Home Affordable Modifications — there are four quick avenues of information.

    1) The federal government has set up a detailed borrower Q&A web link at http://www.financialstability.gov/docs/

    borrower_qa.pdf that acts as the first step to determine eligibility.

    2) Borrowers can also speak directly to Housing and Urban Development-approved housing counselors at 1-800-995-4673. The counselors can help borrowers evaluate their income and expenses and explain options. This counseling service is free.

    3) The state of New Hampshire has also set up a Web site for struggling homeowners at www.HomeHelpNH.org.

    4) Borrowers can also call their loan server, the bank or lending company that takes mortgage payments.

    The Home Affordable Modifications plan is for those who have fallen behind on mortgage payments and face foreclosure, but have the capability to remain in their homes if payments are reduced to 31 percent of gross monthly household income.

    The Home Affordable Refinance will help borrowers looking to refinance and lower their payments, but have been found it difficult because of property value decline.

    Both programs come with strict guidelines designed, administration officials say, to separate the struggling mortgage holder from speculators and the irresponsible. (See accompanying box to find out more about eligibility guidelines.) The goal, both federal and local officials insist, is to stop the spiral of foreclosures and sagging property values.

    “It is imperative that we continue to move with speed to help make housing more affordable and help arrest the damaging spiral in our housing markets,” said Treasury Secretary Timothy Geithner in announcing the guidelines for the plans Wednesday.

    “The more people that can be assisted to stay in their homes, the better it is for everybody, the housing market and our economy,” said Jane Law of the New Hampshire Financing Authority.

    Law said she could only guess at how many people could be helped by the two programs.

    “Every case is so different and that’s what makes it difficult to estimate,” she said.

    But what is known is that the sagging housing market has been a major factor in the current economic recession. Supporters of the plan hope it will help lead to a floor in the housing market.

    “The core of our economic problems is primarily due to a drop in the value of real estate,” said Sen. Judd Gregg, R-N.H. Despite it’s hefty price tag, Gregg supports the Obama administration’s “aggressive plan” because “stabilizing the housing market is crucial” to helping stop the economic slide.

    While New Hampshire and Maine haven’t been hit as hard as states such as Arizona, Florida or California, the foreclosure numbers have risen dramatically.

    According to the New Hampshire Housing Finance Authority, Rockingham County foreclosures have risen from 66 in 2004 to 805 in 2008. Overall, 3,563 foreclosure deeds were filed in New Hampshire in 2008, up more than 700 percent from 448 in 2005. Maine had 2,851 foreclosure filings in 2008, an almost 900 percent increase from 2007. York County had 86 properties in foreclosure in January. Both states have seen a rise in so-called “short sales” in which homeowners and lenders agree to sell a property far below the value of the mortgage.

    “President Obama’s plan is aimed preventing millions of foreclosures, which are the root cause of the downward spiral in property values,” said Sen. Jeanne Shaheen, D-N.H. “This is an issue of deep concern to me and I believe we must take action to help New Hampshire families stay in their homes and protect responsible homeowners who have seen their home values fall through no fault of their own.”

    The Making Home Affordable plan would target $75 billion for lenders and borrowers to restructure or refinance as many as 9 million at-risk mortgages, inject $200 billion into the mortgage giants Fannie Mae and Freddie Mac, which the federal government took over last summer, for lending capital. The administration also is supporting legislation making the rounds in Congress that would allow bankruptcy judges to rewrite mortgages for homeowners in bankruptcy.

    Gregg said the crisis is impacting people’s sense of personal worth and has partially crippled the overall credit market. He believes the federal government will do more to help and is working on legislation to offer a “low-mortgage window” for refinancing and home buying to help stimulate activity.

    “What we need to do is get the inventory sold and get value underneath the market,” he said.

    Citizens Bank, one of the state’s largest financial institutions, said it has already seen a lot of contact activity from its customers since the guidelines were released. Spokesperson Kathleen Reardon said it was still too early to determine how many might be helped.

    “We’re reviewing the program and plan to participate,” she said.

    But one local bank doesn’t expect to see an increase in inquiries.

    “Given the favorable drop in interest rates, we like everybody have seen a very high volume of refinancing,” said Jim Brannen, the chief financial officer of Federal Savings Bank in Dover. “I think that property values (in the Seacoast region) have held up a little better than in other parts of the state and country. Because we have more conservative lending practices, when our customers come in to refinance, they are generally speaking in better (financial) shape.”

    Federal Savings Bank issued no subprime loans and Brannen said “our levels of default and delinquency are very low and manageable.”

    While the foreclosure rescue plan has generated a fair amount of criticism for bailing out reckless mortgage holders at the expense of the vast majority of Americans who have kept up with payments and acted responsibly, the guidelines issued by the Obama administration reveal a set of strict guidelines designed not to save every bad mortgage or those “underwater” (whose mortgage value exceeds their property value.)

    Jane Law at the New Hampshire Housing Authority said the plan offers a wide range of financial incentives for both borrowers and lenders to make the program work. Law said the plans mandate a three-month probation period for borrowers to ensure their commitment.

    Also, the federal government will offer mortgage-servicing companies up-front incentive payments of $1,000 for every loan they modify and follow-up payments of $1,000 annually for the first three years if the borrower remains current. For the borrower, the government will also pay $1,000 a year to directly reduce the borrower’s loan amount — in essence adding to the homeowner’s equity — if the borrower makes payments on time for five years.

    Federal officials are warning against scams likely to emerge. The loan refinancing and modification application process is free and any person or company offering loan modification or refinancing services for a fee should be avoided.

    Obama’s Stocks and Bonds Bear Market

    Even $9.00 an hour jobs are being filled by older applicants and high paying jobs are lost. Retail jobs are disappearing at a faster rate in this recession than in any other since the U.S. government began keeping track in 1939.

    From the “We could see this coming” category,

    Senate Banking Committee Chairman Christopher Dodd is moving to allow the Federal Deposit Insurance Corp. to temporarily borrow as much as $500 billion from the Treasury Department.

    Last week, the FDIC proposed raising fees on banks in order to build up its deposit insurance fund, which had just $19 billion at the end of 2008. That idea provoked protests from banks, which said such a burden would worsen their already shaken condition. The Dodd bill, if it becomes law, would represent an alternative source of funding.

    It appears that the only entity that isn’t broke yet is the government.

    Obama’s Bear Market.

    — The Dow Jones Industrial Average has fallen 20 percent since Inauguration Day, the fastest drop under a newly elected president in at least 90 years, according to data compiled by Bloomberg. The gauge has lost 53 percent from its October 2007 record of 14,164.53, slipping 4.1 percent to 6,594.44 yesterday. More than $1.6 trillion has been erased from U.S. equities since Jan. 20 as mounting bank losses and rising unemployment convinced investors the recession is getting worse.

    Treasuries are struggling with a potential oversupply.

    Treasuries fell this morning as traders focused on the $63 billion in notes and bonds to be sold next week after a government report showed the economy shed jobs and unemployment climbed to the highest level in more than 25 years.

    Government debt has handed investors a 2.5 percent loss so far this year as the U.S. embarks on the sale of more than $2 trillion in debt to steer the nation out of recession.

    Gold is giving back hard-earned gains.

    ( Bloomberg ) — Some investors have become concerned about possible future inflation as governments and central banks spend trillions of dollars and lower interest rates in an effort to rescue financial companies and revive economies. Those steps have yet to help the U.S. economy, the world’s largest, to revive growth or stem job cuts as companies seek to reduce costs in response to tumbling sales. As long as the economy is flat on its back, inflation may not have the effect that is anticipated.

    Japanese sentiment a sign that they are near a bottom?

    Japanese stocks retreated, extending a weekly decline, on concern a shortage of funds could spark collapses in the automotive and electronics industries. “Investors are getting more and more worried about businesses’ survival as the end of the fiscal year draws near,” said Yoshihiro Ito , senior strategist at Tokyo-based Okasan Asset Management Co., which oversees about $9.3 billion. “The deterioration of Japan’s economy is way beyond that of other nations, and the market has entered a tunnel with no exit.”

    The Shanghai Index optimistic prospects may be dimming.

    China’s stocks fell, paring the benchmark index’s weekly gain, as commodity producers and shipping lines slid on concern stimulus spending won’t be enough to offset the collapse in the nation’s exports. Collapsing exports have dragged China, the world’s third- largest economy, to its weakest growth in seven years. Optimism government stimulus spending will revive growth has driven the Shanghai Composite 20 percent higher this year, the best performer among 91 global stock gauges tracked by Bloomberg.

    The dollar is due for a pullback,

    — The dollar fell against the euro and the yen before a government report that may show the U.S. lost the most jobs last month since 1949.

    The U.S. currency weakened for a second day against the yen before the Labor Department report, which may show the unemployment rate rose in February to a 25-year high as payrolls fell by 650,000.

    Housing plan “kicking the can down the road.”.

    The Obama administration yesterday sketched in the details of its most ambitious attempt to reduce foreclosures and stabilize the beleaguered housing market at the root of the economic meltdown. The program has two key elements: a refinancing program for borrowers with little equity in their homes but current on their loans, and a $75 billion program to help reduce mortgage payments for struggling borrowers. Unfortunately, it does not address that most homeowners who are in trouble have negative equity. This plan carries more hope than substance.

    You’ve got oil!

    The Energy Information Administration tells us about a relatively recent discovery of shale oil in the Western States. “The Bakken Formation contains a major onshore unconventional oil resource in Montana, North Dakota, and Saskatchewan, Canada. The Bakken shales produce a light oil that is generally desirable because it offers a high yield of gasoline and other key petroleum products. Proved oil reserves in Montana and North Dakota grew from 831 million barrels in 2006 to 892 million barrels in 2007.”

    A lack of drawdown is keeping gas supplies high.

    The Energy Information Agency’s Natural Gas Weekly Update reports that a late winter cold spell in the lower 48 states and a winter storm in the east has temporarily boosted natural gas prices. But the drawdown of 102 billion cubic feet (BCF) was less than the prior 5 year average of 121 BCF and smaller than the 139 BCF drawdown last year.

    Are our banks worth saving?

    Our politicians want to blame our banking problems on the greedy executives. There is plenty of blame that can be pointed there. However, our financial system has been rigged by a maze of laws and regulations that has flawed the system so badly that it may not be worth saving. Michael Rozeff of LewRockwell.com has written an article that may help understand why the current system may not be worth saving.

    Ground zero of the economic depression is the banking system – worldwide. The system is collapsed, exploded, demolished, gone, ruined, kaput. The global banking system was a house of cards, and it has fallen. Governments and central banks everywhere do not yet realize this. They are attempting to rebuild the house from the pieces and scraps scattered far and wide. Better to salvage the pieces that still work and use them in an entirely new system than attempt to rebuild this one on the same cracked foundation and along the same flawed lines that produced this wreck.

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