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Maze rule
Rulestring 12345/3
Rule integer 31752
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 resembles Conway's Game of Life in some ways, but it is rather more difficult for cells to die off, and random starting patterns tend to evolve into complex growing 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 nine or fewer cells in the maze rule.[2] 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. Similarly, every still life in the maze rule will also be a still life in the Life without death 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 and/or width) is a still life.

Size Count Image Links
1 0
2 2 Maze2cellstilllifes.png Download RLE: click here
3 1 Maze3cellstilllifes.png Download RLE: click here
4 5 Maze4cellstilllifes.png Download RLE: click here
5 7 Maze5cellstilllifes.png Download RLE: click here
6 18 Maze6cellstilllifes.png Download RLE: click here
7 40 Maze7cellstilllifes.png Download RLE: click here
8 197 Maze8cellstilllifes.png Download RLE: click here
9 669 Maze9cellstilllifes.png Download RLE: click here


The smallest period 2 oscillator is an on-off that 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


  1. "Maze (B3/S12345)". David Eppstein. Retrieved on March 16, 2009.
  2. Computed using the EnumStillLifes.c script located here.

External links

  • Maze at David Eppstein's Glider Database