Cellular automaton simulation programs by supported rulespaces

This is an incomplete, messy table of multiple cellular automaton simulator programs with the rulespaces they natively support.

Grids

Euclidean regular

{∞}

One-dimensional cellular automata, run on the cells of an apeirogon.

2-state

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Cell	Life32	WolframAlpha
	range 1^{[n 1]}	range 1^{[n 1]}	No	?	?	range ?-?^{[n 2]}	?	?	?	range 0-?

Isotropic non-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Cell	Life32	WolframAlpha
	range 1^{[n 1]}	range 1^{[n 1]}	No	?	?	range ?-?^{[n 2]}	?	?	?	range 0-?^{[n 2]}

Non-isotropic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Cell	Life32	WolframAlpha
	range 1	range 1	No	?	?	range ?-?	?	?	?	range 0-?

n-state

{4,4}

Two-dimensional cellular automata, run on the cells of a square grid.

2-state

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
von Neumann	range 1-500^{[n 3]}	range 1-500^{[n 3]}	range 1^{[n 4]}	range 1-?	?	range 1-10^{[n 5]}	?^{[n 6]}	range 1-2^{[n 7]}	range 1-?	No
Moore	range 1-500^{[n 3]}	range 1-500^{[n 3]}	range 1-5^{[n 3]} range 1-7^{[n 8]}	range 1-?	?	range 1-10^{[n 3]}^{[n 5]}	range 1	range 1-2^{[n 7]}	range 1-?	No
cross	range 1-500	range 1-500	No	range 1-?	?	No	?^{[n 6]}	range 1-2^{[n 7]}	?	No
saltire	range 1-500	range 1-500	No	range 1-?	?	No	?^{[n 6]}	range 1-2^{[n 7]}	?	No
star	range 1-500	range 1-500	No	range 1-?	?	No	?^{[n 6]}	range 1-2^{[n 7]}	?	No
hash	range 1-500	range 1-500	No	range 1-?	?	No	?^{[n 6]}	range 1-2^{[n 7]}	?	No
checkerboard	range 1-500	range 1-500	No	range 1-?	?	No	?^{[n 6]}	range 1-2^{[n 7]}	?	No
L²	range 1-500	range 1-500	No	range 1-?	?	No	?^{[n 6]}	range 1-2^{[n 7]}	?	No
circular	range 1-500	range 1-500	No	range 1-?	?	No	?^{[n 6]}	range 1-2^{[n 7]}	?	No

Isotropic non-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
range 1 von Neumann	Yes^{[n 4]}	Yes^{[n 4]}	Yes^{[n 4]}	Yes^{[n 9]}	?	Yes^{[n 9]}	?	?	?	No
range 1 Moore	Yes	Yes	Yes	Yes	?	Yes^{[n 9]}	?	?	?	No
exploded Moore	No	No	C2E1 C1E3	C2E1 C1E3	?	?	?	?	?	No
range 2 von Neumann	Multistate emulation only	Multistate emulation only	Yes	Yes	?	?	?	?	?	No

Non-isotropic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
Margolus	Multistate emulation only	Yes	No	Yes	?	Yes	?	?	?	No
range 1 von Neumann	Yes	Yes	No	Yes^{[n 9]}	?	Yes^{[n 9]}	?	?	?	No
range 1 Moore	Yes	Yes	No	Yes^{[n 9]}	?	Yes^{[n 9]}	?	?	?	No
range 2 von Neumann	Multistate emulation only	Multistate emulation only	No	Yes^{[n 9]}	?	?	?	?	?	No
Custom OT neighbourhood	range 1-500	range 1-500	No	range 1-?	?	No	?	range 1-2	?	No
Naive rules	Multistate emulation only	Multistate emulation only	No	Yes	?	?	?	?	?	No

3-state

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
BSFKL	Ruletables only	Ruletables only	Yes	Ruletables only	?	?	?	?	?	No
range 1 Moore	Ruletables only	Ruletables only	Ruletables only	Ruletables only	?	?	?	?	?	No

Isotropic non-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
range 1 Moore	Ruletables only	Ruletables only	Ruletables only	Ruletables only	?	?	?	?	?	No

16-state

Non-isotropic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
Partitioned cellular automata	Ruletables only	Yes	No	No	?	?	?	?	?	No

n-state

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
Cyclic	No	No	No	No	?	range 1-10 states ?-?	?	?	?	No
Rock-paper-scissors	No	No	No	No	?	?	Yes	?	?	No

n-state extensions of 2-state

All of the cases that are supported for 2-state also support extensions (if both the cases and extensions are themselves natively supported) unless mentioned otherwise.

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
Generations	states 2-255	states 2-255	states 2-?	states 2-?^{[n 10]}	?	states 2-?^{[n 10]}	?	?	?	No
Extended Generations	Ruletables only	Ruletables only	states 2-?^{[n 11]}	states 2-?^{[n 10]}	?	?	?	?	?	No
Deficient rules	Ruletables only	Ruletables only	states 2-?^{[n 11]}	states 2-?^{[n 10]}	?	?	?	?	?	No

Isotropic non-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
Generations	states 2-255	states 2-255	states 2-?	states 2-?^{[n 10]}	?	Weighted Generations states 2-?^{[n 10]}	?	?	?	No
Extended Generations	Ruletables only	Ruletables only	states 2-?^{[n 11]}	states 2-?^{[n 10]}	?	?	?	?	?	No
Deficient rules	Ruletables only	Ruletables only	states 2-?^{[n 11]}	states 2-?^{[n 10]}	?	?	?	?	?	No

Non-isotropic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
Generations	states 2-255	states 2-255	No	?	?	?	?	?	?	No
Extended Generations	Ruletables only	Ruletables only	No	?	?	?	?	?	?	No
Deficient rules	Unclear how deficient rules can generalize to non-isotropic rules

{6,3}

Two-dimensional cellular automata, run on the cells of a hexagonal grid.

2-state

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Hexagonal Cell	Life32	WolframAlpha
tripod	range 1-500	range 1-500^{[n 3]}	No	?	?	?	?	range 1-2^{[n 7]}	?	No
asterisk	range 1-500^{[n 3]}	range 1-500^{[n 3]}	range 1	?	?	?	?	range 1-2^{[n 7]}	?	No
hexagonal	range 1-500^{[n 3]}	range 1-500^{[n 3]}	range 1	?	?	?	?	range 1-2^{[n 7]}	?	No

Isotropic non-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Hexagonal Cell	Life32	WolframAlpha
range 1 hexagonal	Via MAP strings	Yes	Yes	Yes	?	Yes^{[n 9]}	?	?	?	No

Non-isotropic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Hexagonal Cell	Life32	WolframAlpha
range 1 hexagonal	Yes	Yes	No	Yes^{[n 9]}	?	Yes^{[n 9]}	?	?	?	No
Custom OT neighbourhood	range 1-500	range 1-500	No	range 1-?	?	No	?	range 1-2	?	No

n-state extensions of 2-state

All of the cases that are supported for 2-state also support extensions (if both the cases and extensions are themselves natively supported) unless mentioned otherwise.

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Hexagonal Cell	Life32	WolframAlpha
Generations	states 2-255	states 2-255	states 2-?	states 2-?^{[n 10]}	?	states 2-?^{[n 10]}	?	?	?	No
Extended Generations	Ruletables only	Ruletables only	No	?	?	?	?	?	?	No
Deficient rules	Ruletables only	Ruletables only	No	?	?	?	?	?	?	No

Isotropic non-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Hexagonal Cell	Life32	WolframAlpha
Generations	states 2-255	states 2-255	states 2-?	states 2-?^{[n 10]}	?	Weighted Generations states 2-?^{[n 10]}	?	?	?	No
Extended Generations	Ruletables only	Ruletables only	No	?	?	?	?	?	?	No
Deficient rules	Ruletables only	Ruletables only	No	?	?	?	?	?	?	No

Non-isotropic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Hexagonal Cell	Life32	WolframAlpha
Generations	states 2-255	states 2-255	No	?	?	?	?	?	?	No
Extended Generations	Ruletables only	Ruletables only	No	?	?	?	?	?	?	No
Deficient rules	Unclear how deficient rules can generalize to non-isotropic rules

{3,6}

Two-dimensional cellular automata, run on the cells of a triangular grid.

2-state

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Triangular Cell	Life32	WolframAlpha
edges	range 1^{[n 12]}	range 1	No	range 1	?	?	?	?	?	No
inner	range 1^{[n 12]}	range 1	No	range 1	?	?	?	?	?	No
outer	range 1^{[n 12]}	range 1	No	range 1	?	?	?	?	?	No
vertices	range 1^{[n 12]}	range 1	No	range 1	?	?	?	?	?	No
Moore	range 1-500	range 1-500^{[n 3]}	No	range 1-?	?	?	?	?	?	No

Non-isotropic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Triangular Cell	Life32	WolframAlpha
Custom OT neighbourhood	range 1-500	range 1-500	No	range 1-?	?	No	?	?	?	No

n-state extensions of 2-state

All of the cases that are supported for 2-state also support extensions (if both the cases and extensions are themselves natively supported) unless mentioned otherwise.

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Triangular Cell	Life32	WolframAlpha
Generations	states 2-255	states 2-255	No	?	?	?	?	?	?	No
Extended Generations	No	No	No	?	?	?	?	?	?	No
Deficient rules	No	No	No	?	?	?	?	?	?	No

Non-isotropic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Triangular Cell	Life32	WolframAlpha
Generations	states 2-255	states 2-255	No	?	?	?	?	?	?	No
Extended Generations	No	No	No	?	?	?	?	?	?	No
Deficient rules	Unclear how deficient rules can generalize to non-isotropic rules

{4,3,4}

Three-dimensional cellular automata, run on the cells of a cubic grid.

{4,3,3,4}

Four-dimensional cellular automata, run on the cells of a tesseractic grid.

2-state

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Cell	Life32	WolframAlpha
Moore	No	No	No	No	No	No	range 1	No	No	No

n-state extensions of 2-state

All of the cases that are supported for 2-state also support extensions (if both the cases and extensions are themselves natively supported) unless mentioned otherwise.

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Cell	Life32	WolframAlpha
Generations	No	No	No	No	No	No	states 2-?	No	No	No

{3,4,3,3}

Four-dimensional cellular automata, run on the cells of a 24-cell grid.

{3,3,4,3}

Four-dimensional cellular automata, run on the cells of a 16-cell grid.

{4,3,3,3,4}

Five-dimensional cellular automata, run on the cells of a penteractic grid.

2-state

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Cell	Life32	WolframAlpha
Moore	No	No	No	No	No	No	range 1	No	No	No

n-state extensions of 2-state

All of the cases that are supported for 2-state also support extensions (if both the cases and extensions are themselves natively supported) unless mentioned otherwise.

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Cell	Life32	WolframAlpha
Generations	No	No	No	No	No	No	states 2-?	No	No	No

Notation extensions

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Cell	Life32	WolframAlpha
[Rule]History	Yes	Yes	No	Yes	?	?	?	?	?	No
[Rule]Super	Yes	Yes	No	No	?	?	?	?	?	No

Notes

↑ ^1.0 ^1.1 ^1.2 ^1.3 As a subset of elementary Wolfram CA
↑ ^2.0 ^2.1 ^2.2 Possibly as a subset of other supported 1D rulespaces
↑ ^3.00 ^3.01 ^3.02 ^3.03 ^3.04 ^3.05 ^3.06 ^3.07 ^3.08 ^3.09 ^3.10 ^3.11 Has a simpler notation for the range-1 case
↑ ^4.0 ^4.1 ^4.2 ^4.3 via Moore isotropic non-totalistic notation
↑ ^5.0 ^5.1 Consecutive birth/survival transitions (Larger than Life) only for ranges above 2
↑ ^6.0 ^6.1 ^6.2 ^6.3 ^6.4 ^6.5 ^6.6 ^6.7 "Large Neighborhood Totalistic Cellular Automata" may allow for this - testing needed
↑ ^7.00 ^7.01 ^7.02 ^7.03 ^7.04 ^7.05 ^7.06 ^7.07 ^7.08 ^7.09 ^7.10 ^7.11 For Java Cell applications, neighbourhoods are manually specified and not systematically generated
↑ Consecutive birth/survival transitions (Larger than Life) only for ranges above 5
↑ ^9.00 ^9.01 ^9.02 ^9.03 ^9.04 ^9.05 ^9.06 ^9.07 ^9.08 ^9.09 ^9.10 via Weighted Life
↑ ^10.00 ^10.01 ^10.02 ^10.03 ^10.04 ^10.05 ^10.06 ^10.07 ^10.08 ^10.09 ^10.10 ^10.11 Extended neighbourhoods unknown
↑ ^11.0 ^11.1 ^11.2 ^11.3 Only range-1 Moore natively supported, and range-1 von Neumann through its notation
↑ ^12.0 ^12.1 ^12.2 ^12.3 Requires the use of a custom CoordCA neighbourhood

[1Dsubset-1] 1.0 ^1.1 ^1.2 ^1.3 As a subset of elementary Wolfram CA

[poss1Dsubset-2] 2.0 ^2.1 ^2.2 Possibly as a subset of other supported 1D rulespaces

[r1notation-3] 3.00 ^3.01 ^3.02 ^3.03 ^3.04 ^3.05 ^3.06 ^3.07 ^3.08 ^3.09 ^3.10 ^3.11 Has a simpler notation for the range-1 case

[mooresubset-4] 4.0 ^4.1 ^4.2 ^4.3 via Moore isotropic non-totalistic notation

[oldltl-5] 5.0 ^5.1 Consecutive birth/survival transitions (Larger than Life) only for ranges above 2

[possiblehrot-6] 6.0 ^6.1 ^6.2 ^6.3 ^6.4 ^6.5 ^6.6 ^6.7 "Large Neighborhood Totalistic Cellular Automata" may allow for this - testing needed

[specify-7] 7.00 ^7.01 ^7.02 ^7.03 ^7.04 ^7.05 ^7.06 ^7.07 ^7.08 ^7.09 ^7.10 ^7.11 For Java Cell applications, neighbourhoods are manually specified and not systematically generated

[ctgltl-8] Consecutive birth/survival transitions (Larger than Life) only for ranges above 5

[weightedsubset-9] 9.00 ^9.01 ^9.02 ^9.03 ^9.04 ^9.05 ^9.06 ^9.07 ^9.08 ^9.09 ^9.10 via Weighted Life

[unkext-10] 10.00 ^10.01 ^10.02 ^10.03 ^10.04 ^10.05 ^10.06 ^10.07 ^10.08 ^10.09 ^10.10 ^10.11 Extended neighbourhoods unknown

[lowext-11] 11.0 ^11.1 ^11.2 ^11.3 Only range-1 Moore natively supported, and range-1 von Neumann through its notation

[customnotation-12] 12.0 ^12.1 ^12.2 ^12.3 Requires the use of a custom CoordCA neighbourhood

[n 1]

[n 2]

[n 3]

[n 4]

[n 5]

[n 6]

[n 7]

[n 8]

[n 9]

[n 10]

[n 11]

[n 12]

Cellular automaton simulation programs by supported rulespaces

Grids

Euclidean regular

{∞}

2-state

Outer-totalistic

Isotropic non-totalistic

Non-isotropic

n-state

{4,4}

2-state

Outer-totalistic

Isotropic non-totalistic

Non-isotropic

3-state

Outer-totalistic

Isotropic non-totalistic

16-state

Non-isotropic

n-state

n-state extensions of 2-state

Outer-totalistic

Isotropic non-totalistic

Non-isotropic

{6,3}

2-state

Outer-totalistic

Isotropic non-totalistic

Non-isotropic

n-state extensions of 2-state

Outer-totalistic

Isotropic non-totalistic

Non-isotropic

{3,6}

2-state

Outer-totalistic

Non-isotropic

n-state extensions of 2-state

Outer-totalistic

Non-isotropic

{4,3,4}

{4,3,3,4}

2-state

Outer-totalistic

n-state extensions of 2-state

Outer-totalistic

{3,4,3,3}

{3,3,4,3}

{4,3,3,3,4}

2-state

Outer-totalistic

n-state extensions of 2-state

Outer-totalistic

Notation extensions

Notes

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