Difference between revisions of "OCA:Maze"
(→Notable patterns: added RLE/Java links for other two patterns) 
(→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.  +  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 LifeConway 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 infinitelyextensible 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 infinitelyextensible 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. 
Revision as of 00:46, 24 March 2009
Maze  


View animated image  
Rulestring  12345/3 B3/S12345 


Character  Explosive 
Maze is a Lifelike 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 mazelike structures with welldefined walls outlining corridors.
Contents
Notable patterns
The maze rule is explosive, which means that most randomlygenerated 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. 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 infinitelyextensible 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.
Oscillators
The smallest period 2 oscillator has several different possible stators, some of which are shown below.
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.
Similar rules
The most wellknown 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.
References
 ↑ "Maze (B3/S12345)". David Eppstein. Retrieved on March 16, 2009.