Difference between revisions of "OCA:Maze"

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(Still lifes: added note about all conway still lifes being still lifes here)
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===Still lifes===
 
===Still lifes===
Below is a sampling of many small patterns that are still lifes in the maze rule. It is worth noting that, because the only difference between this rule and the standard [[Conway's Game of Life|Conway rule]] is that cells have more ways of staying alive, every pattern that is a still life in standard Life is also a still life in the maze rule.
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Below are all still lifes with eight or fewer cells in the maze rule. It is worth noting that, because the only difference between this rule and the standard [[Conway's Game of Life|Conway rule]] is that cells have more ways of staying alive, every pattern that is a still life in standard Life is also a still life in the maze rule.
  
 
Other notable still lifes include the infinitely-extensible diagonal line. Also, any diamond in which every other cell is alive (i.e. any barge that is extended in either length ''or'' width) is a still life.
 
Other notable still lifes include the infinitely-extensible diagonal line. Also, any diamond in which every other cell is alive (i.e. any barge that is extended in either length ''or'' width) is a still life.
[[Image:maze_still_lifes.png|framed|center|Some small still lifes.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=mazestilllifes click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=mazestilllifes.rle click here] ]]
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{| class="wikitable" style="margin-left:auto;margin-right:auto;"
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|-
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! Size
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! Count
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! Image
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|-
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| 1
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| 0
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|
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|-
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| 2
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| 2
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| [[Image:maze2cellstilllifes.png]]
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|-
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| 3
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| 1
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| [[Image:maze3cellstilllifes.png]]
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|-
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| 4
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| 5
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| [[Image:maze4cellstilllifes.png]]
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|-
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| 5
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| 7
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| [[Image:maze5cellstilllifes.png]]
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|-
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| 6
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| 18
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| [[Image:maze6cellstilllifes.png]]
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|-
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| 7
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| 41
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| [[Image:maze7cellstilllifes.png]]
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|-
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| 8
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| 197
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| [[Image:maze8cellstilllifes.png]]
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|}
  
 
===Oscillators===
 
===Oscillators===

Revision as of 17:27, 25 March 2009

Maze
Maze rule
Rulestring 12345/3
B3/S12345
Character Explosive

Maze is a Life-like cellular automaton in which cells survive from one generation to the next if they have at least 1 and at most 5 neighbours. Cells are born if they have exactly 3 neighbours. Because of this, many small patterns behave the same as they would in Conway's Game of Life. In general, any pattern that does not have a living cell adjacent to 1, 4, or 5 other living cells in any of its generations will behave identically under both rules. Because this restriction is satisfied by very few large patterns, evolution under the maze rule differs greatly from evolution under the standard Life rule in general.

This rule is notable because random starting patterns tend to evolve into complex maze-like structures with well-defined walls outlining corridors.

Notable patterns

The maze rule is explosive, which means that most randomly-generated starting patterns will explode in all directions. Nonetheless, there are many still lifes and oscillators under this rule. It has no known spaceships.[1]

Still lifes

Below are all still lifes with eight or fewer cells in the maze rule. It is worth noting that, because the only difference between this rule and the standard Conway rule is that cells have more ways of staying alive, every pattern that is a still life in standard Life is also a still life in the maze rule.

Other notable still lifes include the infinitely-extensible diagonal line. Also, any diamond in which every other cell is alive (i.e. any barge that is extended in either length or width) is a still life.

Size Count Image
1 0
2 2 Maze2cellstilllifes.png
3 1 Maze3cellstilllifes.png
4 5 Maze4cellstilllifes.png
5 7 Maze5cellstilllifes.png
6 18 Maze6cellstilllifes.png
7 41 Maze7cellstilllifes.png
8 197 Maze8cellstilllifes.png

Oscillators

The smallest period 2 oscillator has several different possible stators, some of which are shown below.

Some small period 2 oscillators.
Manipulate via Java: click here
Download RLE: click here

Other patterns

One wickstretcher that commonly appears from random starting configurations is shown below. Its period is 12 and it travels at speed c/3. It can be stabilized on the left edge in many different ways.

A common wickstretcher.
Manipulate via Java: click here
Download RLE: click here

Similar rules

The most well-known related rule is known as mazectric, which has rulestring 1234/3. That is, it is the same as the maze rule except that cells don't survive if they have 5 neighbours. This results in maze patterns that tend to have longer and straighter corridors.

Generation 235 of the evolution of a 10×10 square of random cells under the mazectric rule

References

  1. "Maze (B3/S12345)". David Eppstein. Retrieved on March 16, 2009.