OCA:Maze

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Maze
x=64, y = 64, rule = B3/S12345 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated pseudorandom soup
View static image
View animated image
Rulestring 12345/3
B3/S12345
Rule integer 31752
Character Explosive
Black/white reversal B0128/S01234678

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 Download RLE: click here
3 1 Download RLE: click here
4 5 Download RLE: click here
5 7 Download RLE: click here
6 18 Download RLE: click here
7 40 Download RLE: click here
8 197 Download RLE: click here
9 669 Download RLE: click here

Oscillators

The smallest period 2 oscillator is an on-off that has several different possible stators, some of which are shown below.

x = 28, y = 5, rule = B3/S12345 2obo3b2obo4b2ob2o3b2ob2o$bobo4bobo5bobo5bob2o$o6bo2b2o3bo2b2o3bo2bo$o 2bo3bo3bo3bo3bo3bo3bo$2b2o5b2o6b2o6b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ AUTOSTART GPS 2 ]]
Some period 2 oscillators
(click above to open LifeViewer)
RLE: here Plaintext: 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.

x = 6, y = 8, rule = B3/S12345 2o$b3o$bob2o$3b3o$3b2o$bobo$b3o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
A common wickstretcher
(click above to open LifeViewer)
RLE: here Plaintext: here

Similar rules

Mazectric

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. On October 20th, 2026, this rule has been proven omniperiodic using drifters.

Mazectric
x=64, y = 64, rule = B3/S1234 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated pseudorandom soup
View static image
Rulestring 1234/3
B3/S1234
Rule integer 15368
Character Explosive
Black/white reversal B01238/S01234678
Generation 235 of the evolution of a 10×10 square of random cells under the mazectric rule
#O Katrina #C Oscillators from period 1 to period 16 in Mazectric. #C Using this signal and turner, it is possible to construct an oscillator of any period above 6. #C https://conwaylife.com/forums/viewtopic.php?p=238059#p238059 x = 479, y = 262, rule = B3/S1234 243b2ob2o5b2o5b2ob2o2b2o2bo$242bo2b2o2b2obo2bo3bob2o3bo2bo2bo$241bo2bo 2b2obob3obobo4b3o2bo4bo$241bob2obob6o2bob6o2b2ob5o$243b2ob2o2b3o5b2ob 2ob2ob2obobo$241bo2bo6bo2b2ob5obo4bobo3bo$240bo3b5o2bobobo2bobo7bo3bob o$245b4o4bobob2ob3o6b4o$229b2ob2obo4bo3b5o2bobobo2bobo7bo3bobo$219b2ob o6b3ob3o5bo2bo6bo2b2ob5obo4bobo3bo$219b2obo7b3o10b2ob2o2b3o5b2ob2ob2ob 2obobo$212b2o7b4o4bobo2b2o5bob2obob6o2bob6o2b2ob5o$212bobo4b4o6bobo3bo 5bo2bo2b2obob3obobo4b3o2bo4bo$211b4o6bo12bo7bo2b2o2b2obo2bo3bob2o3bo2b o2bo$205b2o4b2o8bo11bo9b2ob2o5b2o5b2ob2o2b2o2bo16$118bo$119bo$118b2o$ 117bo2b2ob2o$118b2obobo$123b4o$113bob2obo3bo3bo3bo$113bob2o2b2o2bo2b2o bo$111bobo6bob4ob3obo$108bo2bo3b5o2bob3o3bo2bo$109bob2o3bobo3bobo2bo2b 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o4bo2bo2bo3bobo$37bob2o2bo2bobo3bobo3b2obo67bob2o2bo2bobo3bobo3b2obo 80bob2o2bo2bobo3bobo3b2obo87bob2o2bo2bobo3bobo3b2obo60b2o2bo2bobo3bobo 3b2obo$37bo2bo3bo3bo2b5o3bo2bo66bo2bo3bo3bo2b5o3bo2bo79bo2bo3b3obo2b5o 3bo2bo86bo2bo3bo3bo2b5o3bo2bo58bobo3bo3bo2b5o3bo2bo$39bob3o3b2obo6bobo 71bob3o3b2obo6bobo84bob3ob4obo6bobo91bob3o3b2obo6bobo61bo2b3o3b2obo6bo bo$41bob2o2bo2b2ob3obo75bob2o2bo2b2o2b2obo88bob2o2bo2b2o2b2obo95bob2o 2b2ob2o2b2obo64bobob2o2bo2b2obobobo$40bo3bo3bo2b5obo74bo3bo3bob2o2b2ob o87bo3bo3bo5b2obo94bo3bo3bo5b2obo65bo3bo3bo6bobo$44b4o3b3o82b4o2b2o97b 4o108b4o79b4o$47bobob2o86bobob2o99bobobo107bobobo78bobobo$46b2ob2o2bo 84b2ob2o2bo97b2ob2o2bo104b2ob2o2bo75b2ob2o2bo$51b2o90b2o103b2o110b2o 81b2o$51bo91bo104bo111bo82bo$52bo91bo104bo111bo82bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 1 THUMBSIZE 2 GPS 60 HEIGHT 500 ]]
Signal and turner-based adjustable oscillator for periods > 6.
(click above to open LifeViewer)
RLE: here Plaintext: here

Mice

By adding seven to the birth condition, you get "mice" running through the mazes of Maze or Mazectric.

Maze with Mice
x=64, y = 64, rule = B37/S12345 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated pseudorandom soup
Rulestring 12345/37
B37/S12345
Rule integer 31880
Character Explosive
Black/white reversal B01238/S0234678
Mazectric with Mice
x=64, y = 64, rule = B37/S1234 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated pseudorandom soup
Rulestring 1234/37
B37/S1234
Rule integer 15496
Character Explosive
Black/white reversal B0128/S0234678

References

  1. ↑ Maze (B3/S12345) at David Eppstein's Glider Database
  2. ↑ Computed using the EnumStillLifes.c script located here.
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