Difference between revisions of "OCA:Maze"

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Below is a sampling of many small patterns that are still lifes in the maze rule. Several small still lifes from [[Conway's Game of Life]] are also still lifes in this rule, and they include [[block]], [[tub]], [[barge]], [[ship]], [[boat]], [[loaf]], [[beehive]], [[snake]], and [[aircraft carrier]].
 
Below is a sampling of many small patterns that are still lifes in the maze rule. Several small still lifes from [[Conway's Game of Life]] are also still lifes in this rule, and they include [[block]], [[tub]], [[barge]], [[ship]], [[boat]], [[loaf]], [[beehive]], [[snake]], and [[aircraft carrier]].
  
Other notable
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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.
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[[Image:maze_still_lifes.png|framed|center|Some small still lifes.]]
  
{|
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===Oscillators===
|-
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The smallest [[period]] 2 oscillator has several different possible [[casing]]s, some of which are shown below.
|[[Image:maze_still_lifes.png|framed|center|Some small still lifes.]]
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[[Image:maze_p2.gif|framed|center|Some small period 2 oscillators.]]
|}
 
  
 
==Similar rules==
 
==Similar rules==

Revision as of 16:27, 17 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.

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 is a sampling of many small patterns that are still lifes in the maze rule. Several small still lifes from Conway's Game of Life are also still lifes in this rule, and they include block, tub, barge, ship, boat, loaf, beehive, snake, and aircraft carrier.

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.

Some small still lifes.

Oscillators

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

Some small period 2 oscillators.

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.