Cellular Automata rules lexicon

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Family: Rules tables

Type: totalistic or outer totalistic rules table

"Rules tables" game allows defining totalistic rules by creating special transitions tables. Rules tables remove all limits from totalistic rules, allowing defining any rules, where states of cells can advance, but can also jump, both forward and back.

The idea of the rules table is simple. It describes what new state should get the cell having state S, providing it has N firing neighbors.

Rules table notation

The notation of Rules table has the "N,M,F,S" form, where:
N - specifies the neighborhood type: 1 stands for  Moore, 2 for von Neumann neighborhood.
M - specifies activity of the center (middle) cell. 1 is on, 0 is off.
F - specifies if the full 1st bitplane (all odd states) is considered to be firing (can give birth). This flag was introduced in order to provide compatibility with CelLab by Rudy Rucker and John Walker.
S - specifies the whole table, row by row, as one string. Trailing 0s can be removed.

Examples:

The Conway's Life: (1,0,0,) 0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0

  0 1 2 3 4 5 6 7 8

explanation

0 0 0 0 1 0 0 0 0 0 dead cells with 3 alive neighbors turn alive
1 0 0 1 1 0 0 0 0 0 alive cells with 2 and 3 neighbors survive

The Brian's Brain: (1,0,0,) 0,0,1,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0

  0 1 2 3 4 5 6 7 8

explanation

0 0 0 1 0 0 0 0 0 0 dead cells with 2 firing neighbors turn alive
1 2 2 2 2 2 2 2 2 2 all cells in state 1 get older
2 0 0 0 0 0 0 0 0 0 all cells in state 2 must die

 

MJCell Java applet is able to run all rules from this group.

MCell built-in Rules tables

Name Character Description Rule table (N,M,F,S)
Balloons Exploding A very striking rule which is yet another step past Brian's Brain. Brain's haulers build up connected regions as in Brain, but now the regions form membranes, grow, burst, and are eaten.
A rule by Brian Silverman.
1,0,1,
0,0,15,0,0,0,5,0,0,0,  0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0, 4,4,8,4,4,4,4,4,4,0,  5,5,5,5,5,7,7,9,11, 0,2,2,2,2,2,2,2,2,2,  0,5,5,5,5,5,13,13,9,11, 0,8,8,10,8,8,8,8,8,8,0,  2,2,2,2,2,9,13,9,11,0, 10,10,0,10,10,10,10,10,10,0,  4,14,14,14,14,14,14,14,11,0, 2,12,4,12,12,12,12,12,12,0,  6,6,6,6,13,13,13,9,11,0, 14,14,14,12,14,14,14,14,14,0,  2,2,2,2,2,2,2,2,2
Busy Brain Chaotic A variation of Brian's Brain, with more chaos. The animation looks similar, yet the board is more filled, and patterns produce more sparks.
A rule by George Maydwell.
1,0,0,
0,0,1,2,0,2,2,2,2,0, 2,2,2,1,0,2,2,2,2, 0,0,0,0,0,1,2,2,1,2
Cars Gliding A very amusing rule producing... racing cars of several types! It's fun to watch them driving, smashing, bouncing. The rule features also interesting oscillators.
A rule by Rudy Rucker.
1,0,1,
0,2,15,6,8,2,4,6,8, 0,0,0,0,0,0,0,0,0,0,0, 4,4,4,4,4,4,4,4,4, 0,0,0,0,0,0,0,0,0,0,0, 0,6,6,6,6,6,6,6,6, 0,0,0,0,0,0,0,0,0,0,0, 8,8,8,8,8,8,8,8,8, 0,0,0,0,0,0,0,0,0,0,0, 10,10,10,10,10,10,10,10,10, 0,0,0,0,0,0,0,0,0,0,0, 12,12,12,12,12,12,12,12,12, 0,0,0,0,0,0,0,0,0,0,0, 14,14,14,14,14,14,14,14,14, 0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0, 2,15,15
Cheops Expanding Improved variation of Strangers, showing gliders with an angle of 53 degrees, same as the base angle of the Cheops pyramid.
A rule by Alastair Couper.
1,0,0,
0,4,1,9,8,0,0,0,0,0,  5,0,9,7,0,6,0,9,8,0, 8,0,0,0,0,0,0,0,0,0,  0,0,2,0,0,6,0,0,4,0, 3,0,0,0,3,0,1,0,0,0,  4,0,3,0,9,0,6,1,0,0, 0,5,0,0,0,0,4,1,0,0,  2,7,0,2,6,3,8,4,6,0, 1,0,0,0,0,0,0,0,0,0, 0,0,0,6,7,0,8,5,3
Cooties 2 Exploding A prototype of the "real" Cooties rule, found in Generations family.
A rule by Rudy Rucker.
1,0,1,
0,0,15,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 4,4,4,4,4,4,4,4,4,0, 0,0,0,0,0,0,0,0,0,0, 14,14,14,14,14,14,14,14,14, 0,0,0,0,0,0,0,0,0,0,0, 10,10,10,10,10,10,10,10,10,0, 12,12,15,12,12,12,12,12,12
Crawlers Expanding This rule produces many different small and big creatures crawling around.
A rule by Rudy Rucker.
1,0,1,
0,14,3,8,0,0,0,0,0,0, 2,8,0,6,0,0,3,11,0,0, 0,0,0,10,0,0,0,0,0,0, 0,2,0,11,0,6,0,0,0,0, 6,0,0,0,4,0,9,0,0,0, 6,0,8,0,0,11,10,0,8,0, 10,0,0,0,11,0,0,6,0,0, 0,10,0,0,0,0,5,0,0,0, 2,8,0,0,0,0,0,0,0,0, 6,0,5,14,0,0,0,1,0,0, 0,11,6,0,0,8,8,0,0,0, 8,12,0,0,0,0,0,6,5,0, 8,0,0,0,0,0,8,8,0,0, 1,0,0,2,6,0,6,0,5,0, 0,0,0,0,0,0,0,11,0,0, 0,0,0,0,0,0,0,3,9
EcoLiBra Chaotic This rule is a cross between Life and Brian's Brain. The basic idea is that the cells are divided between dark "sea" cells and light "land" cells. We run Brain in the sea, and on land we run not Life but AntiLife. Six or seven firing Brain cells turn a sea cell into land. Seven "antifiring" Antilife cells turn a land cell into sea.
A rule by Rudy Rucker.
1,0,1,
0,0,7,0,0,0,15,15,0, 0,0,0,0,0,0,0,0,0,0,0, 15,15,15,15,15,2,2,15,15,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 12,12,12,12,12,12,12,12,12, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0, 15,0,15,15,15,2,15,15,15
Empire Chaotic Empire is named rather aptly for the actions of the Life patterns within it: whatever you start off with, it will expand with a chaotic border, take over the world, collapse into warring factions and fleeting calm patches, and eventually stabilise and stagnate.
The effect remains the same whether one uses a 23/3 style input for gens 1 and 2, 7 and 8, or both.
Starting with EcoLiBra and adding the center cell, then finishing lines 2, 7, and 15 with 15, 12, and 15 respectively, one gets a Brain like world which eventually (1,000 or 2,000 gen) grows islands. They end up eating the world.
A rule by Charles A. Rockafellor, March 2000
1,0,1,
0,0,7,1,0,0,15,15,0, 0,0,0,1,1,0,0,0,0, 0,0,15,15,15,15,15,2,2, 15,15,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,12,12, 12,12,12,12,12,12,12,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,15,0,15, 15,15,2,15,15,15
Fire sticks Gliding This rule produces long gliding sticks, often sparkling on one side.
A rule by Rudy Rucker.
1,0,1,
0,0,15,15,0,0,0,0,0,0, 0,0,0,3,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,5,0,0,0,0,0,0, 6,6,0,6,6,6,6,6,6,0, 0,0,0,7,0,0,0,0,0,0, 8,8,6,8,8,8,8,8,8,0, 0,0,0,9,0,0,0,0,0,0, 2,2,8,2,2,2,2,2,2,0, 0,0,0,11,0,0,0,0,0,0, 4,4,10,4,4,4,4,4,4,0, 0,0,0,13,0,0,0,0,0,0, 14,14,12,14,14,14,14,14,14,0, 0,0,0,15,0,0,0,0,0,0, 10,10,14,10,10,10,10,10,10,0, 12,12,0,15,12,12,12,12,12
Historical Life Chaotic This rule duplicates Conway's Life -- all constructions will work identically -- but it leaves a trail of a third type of cell wherever a cell has once been alive. This is useful for placing still lifes to affect a pattern, without having to backtrack continually to find out whether the still life would have interacted with the pattern in previous generations.
A rule by Dave Greene, April 2001.
1,0,1,
0,0,0,1,0,0,0,0,0,0,2,2,1,1, 2,2,2,2,2,0,2,2,2,1,2,2,2,2,2
Ladders Chaotic This rule produces orthogonal ladder-like replicators.
A rule by Rudy Rucker.
1,0,1,
0,6,5,0,0,2,15,5,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,8,7,15,0,15,0,0, 0,0,6,0,0,0,0,0,3,0, 0,0,0,0,0,0,0,0,0,0, 8,0,0,0,0,0,0,0,0,0, 8,4,2,5,6,0,0,0,0,0, 4,0,11,0,0,0,0,0,0,0, 0,0,0,0,0,0,15,4,0,0, 0,8,0,15,5,0,0,0,0,0, 4,10,0,0,4,5,0,0,4,0, 0,8,8,0,0,12,4,6,0,0, 0,0,0,10,2,10,6,6,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,9,0,11,3,0,0, 9,0,0,0,14,0,0,6
Piranha Chaotic A very funny rule, featuring a diagonal piranha-like glider and a replicator.
A rule by Rudy Rucker.
1,0,1,
0,6,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,11,0,0,0,0,0,0,0,0, 7,0,6,0,0,0,0,0,0,0, 0,0,0,3,0,0,0,0,9,0, 0,0,6,0,0,0,0,0,0,0, 0,0,0,0,3,0,0,0,0,0, 5,0,0,0,0,0,0,0,0,0, 8,0,4,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,3,0,0, 0,0,0,0,0,0,0,0,0,0,1
Ran Brain Exploding Another member of the Brian's family. The rule is much less live, and often creates Sierpinski-like patterns.
A rule by Rudy Rucker.
1,0,1,
0,0,5,10,0,0,5,10,0,0, 0,0,5,10,0,0,0,0,15,0, 0,0,0,0,0,15,15,0,0,0, 0,0,14,0,0,0,0,0,0,0, 0,0,4,0,0,0,0,0,0,0, 2,6,2,6,2,6,2,6,2,0, 2,6,2,6,2,6,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,12,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,12,0,0, 0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,14,7
Strangers Gliding The rule produces many funny and surprisingly stable ships. The ships are always gliding, without any flickering of cells.
A rule by Mirek Wojtowicz.
1,0,0,
0,4,1,9,8,0,0,0,0,0,  5,0,9,7,0,6,0,9,8,0, 2,5,0,4,0,0,0,0,0,0,  0,10,2,10,0,6,0,0,4,0, 3,0,10,0,3,0,1,10,0,0,  4,0,3,10,9,0,6,1,0,0, 0,5,0,0,0,0,4,1,0,0,  2,7,0,2,6,3,8,4,6,0, 1,0,0,0,0,0,0,0,0,0,  0,0,0,6,7,0,8,5,3,0, 9,0,0,5,0,4,0,0,5,0,  0,0,0,0,0,0,9,0,0,0
Wire World Stable The cellular automaton WireWorld is attributed to Brian Silverman and was included in his program PHANTOM FISH TANK in 1987. A. K. Dewdney publicized WireWorld in his "Computer Recreations" column (Scientific American, January, 1990).

Cells in WireWorld have one of four possible states: background (0), electron head (1), electron tail (2), and wire (3).
The rules for updating cells are:

- background (0) always remains background.
- electron head (1) always changes to electron tail.
- electron tail (2) always changes to wire.
- wire (3) changes to electron head if one or two of its neighbours are electron heads.

These simple rules allow fairly complicated logic circuits to be constructed.
1,0,0,
0,0,0,0,0,0,0,0,0,0,
2,2,2,2,2,2,2,2,2,0,
3,3,3,3,3,3,3,3,3,0,
3,1,1,3,3,3,3,3,3

 


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Last update: 20 Sep 2001