Cellular automaton simulation programs by supported rulespaces

This is an set of tables 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
1D	range 1^{[subset 1]}	range 1^{[subset 1]}	No	?	?	range ?-?^{[verify 1]}	?	?	?	range 0-?

Isotropic non-totalistic

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

Non-isotropic

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

n-state

Outer-totalistic

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

Isotropic non-totalistic

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

Non-isotropic

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

{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 1]}^{[equivalent 1]}^{[equivalent 2]}	range 1-500^{[n 1]}^{[equivalent 1]}^{[exclude 2]}	range 1^{[subset 3]}	range 1-?	?	range 1-10^{[exclude 3]}	?^{[verify 2]}	range 1-2^{[subset 4]}	range 1	No
Moore	range 1-500^{[n 1]}^{[equivalent 1]}^{[exclude 2]}	range 1-500^{[n 1]}^{[equivalent 1]}^{[exclude 2]}	range 1-5^{[n 1]} range 1-7^{[exclude 4]}	range 1-?	?	range 1-10^{[n 1]}^{[exclude 3]}	range 1	range 1-2^{[subset 4]}	range 1	No
cross	range 1-500^{[exclude 2]}	range 1-500^{[exclude 2]}	No	range 1-?	?	No	?^{[verify 2]}	range 1-2^{[subset 4]}	No	No
saltire	range 1-500^{[exclude 2]}	range 1-500^{[exclude 2]}	No	range 1-?	?	No	?^{[verify 2]}	range 1-2^{[subset 4]}	No	No
star	range 1-500^{[exclude 2]}	range 1-500^{[exclude 2]}	No	range 1-?	?	No	?^{[verify 2]}	range 1-2^{[subset 4]}	No	No
hash	range 1-500^{[exclude 2]}	range 1-500^{[exclude 2]}	No	range 1-?	?	No	?^{[verify 2]}	range 1-2^{[subset 4]}	No	No
checkerboard	range 1-500^{[exclude 2]}	range 1-500^{[exclude 2]}	No	range 1-?	?	No	?^{[verify 2]}	range 1-2^{[subset 4]}	No	No
L²	range 1-500^{[exclude 2]}	range 1-500^{[exclude 2]}	No	range 1-?	?	No	?^{[verify 2]}	range 1-2^{[subset 4]}	No	No
circular	range 1-500^{[exclude 2]}	range 1-500^{[exclude 2]}	No	range 1-?	?	No	?^{[verify 2]}	range 1-2^{[subset 4]}	No	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^{[subset 3]}	Yes^{[subset 3]}	Yes^{[subset 3]}	Yes^{[subset 5]}	?	Yes^{[subset 5]}	?	?	Yes^{[subset 3]}	No
range 1 Moore	Yes^{[equivalent 1]}	Yes^{[equivalent 1]}	Yes	Yes	?	Yes^{[subset 5]}	?	?	Yes	No
exploded Moore	No	No	C2E1 C1E3	C2E1 C1E3	?	?	?	?	No	No
range 2 von Neumann	No^{[emulate 1]}	No^{[emulate 1]}	Yes	Yes	?	?	?	?	No	No

Non-isotropic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
Margolus	No^{[emulate 1]}	Yes^{[exclude 5]}^{[equivalent 3]}	No	Yes	?	Yes	?	?	No	No
range 1 von Neumann	Yes^{[equivalent 1]}	Yes^{[equivalent 1]}	No	Yes^{[subset 5]}	?	Yes^{[subset 5]}	?	?	No	No
range 1 Moore	Yes^{[equivalent 1]}	Yes^{[equivalent 1]}	No	Yes^{[subset 5]}	?	Yes^{[subset 5]}	?	?	No	No
range 2 von Neumann	No^{[emulate 1]}	No^{[emulate 1]}	No	Yes^{[subset 5]}	?	?	?	?	No	No
Custom OT neighbourhood	range 1-500^{[exclude 2]}	range 1-500^{[exclude 2]}	No	range 1-?	?	No	?	range 1-2	No	No
Naive rules	No^{[emulate 1]}	No^{[emulate 1]}	No	Yes	?	?	?	?	No	No

3-state

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
BSFKL	Yes^{[subset 2]}	Yes^{[subset 2]}	Yes	Yes^{[subset 2]}	?	?	?	?	?	No
range 1 Moore	Yes^{[subset 2]}	Yes^{[subset 2]}	Yes^{[subset 2]}	Yes^{[subset 2]}	?	?	?	?	?	No

Isotropic non-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
range 1 Moore	Yes^{[subset 2]}	Yes^{[subset 2]}	Yes^{[subset 2]}	Yes^{[subset 2]}	?	?	?	?	?	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	Yes^{[subset 2]}	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 ?-?	range ?-? states ?-?	?	?	No
Rock-paper-scissors	No	No	No	No	?	?	range ?-? states ?-?	?	?	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^{[exclude 6]}^{[exclude 2]}	states 2-255^{[exclude 6]}^{[exclude 2]}	states 2-?	states 2-?^{[verify 3]}	?	states 2-?^{[verify 3]}	states 2-50	?	?	No
Extended Generations	Yes^{[subset 2]}	Yes^{[subset 2]}	states 2-?^{[exclude 7]}	states 2-?^{[verify 3]}	?	?	?	?	?	No
Deficient	Yes^{[subset 2]}	Yes^{[subset 2]}	states 2-?^{[exclude 7]}	states 2-?^{[verify 3]}	?	?	?	?	?	No
Alternating	Yes^{[subset 2]}	rules 2^{[exclude 8]}	Yes^{[subset 2]}	?	?	?	?	?	?	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^{[exclude 6]}	states 2-255^{[exclude 6]}	states 2-?	states 2-?^{[verify 3]}	?	Weighted Generations states 2-?^{[verify 3]}	?	?	?	No
Extended Generations	Yes^{[subset 2]}	Yes^{[subset 2]}	states 2-?^{[exclude 7]}	states 2-?^{[verify 3]}	?	?	?	?	?	No
Deficient	Yes^{[subset 2]}	Yes^{[subset 2]}	states 2-?^{[exclude 7]}	states 2-?^{[verify 3]}	?	?	?	?	?	No
Alternating	Yes^{[subset 2]}	rules 2	Yes^{[subset 2]}	?	?	?	?	?	?	No

Non-isotropic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Square Cell	Life32	WolframAlpha
Generations	states 2-255^{[exclude 6]}	states 2-255^{[exclude 6]}^{[exclude 9]}	No	?	?	?	?	?	?	No
Extended Generations	Yes^{[subset 2]}	Yes^{[subset 2]}	No	?	?	?	?	?	?	No
Deficient	Unclear how deficient rules can generalize to non-isotropic rules
Alternating	Yes^{[subset 2]}	rules 2	No	?	?	?	?	?	?	No

{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 1]}	No	?	?	?	?	range 1-2^{[subset 4]}	?	No
asterisk	range 1-500	range 1-500	No	?	?	?	?	range 1-2^{[subset 4]}	?	No
hexagonal	range 1-500^{[n 1]}	range 1-500^{[n 1]}	range 1	?	?	?	range 1	range 1-2^{[subset 4]}	?	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^{[subset 5]}	?	?	?	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^{[subset 5]}	?	Yes^{[subset 5]}	?	?	?	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-?^{[verify 3]}	?	states 2-?^{[verify 3]}	states 2-50	?	?	No
Extended Generations	Yes^{[subset 2]}	Yes^{[subset 2]}	No	?	?	?	?	?	?	No
Deficient	Yes^{[subset 2]}	Yes^{[subset 2]}	No	?	?	?	?	?	?	No
Alternating	Yes^{[subset 2]}	rules 2	Yes^{[subset 2]}	?	?	?	?	?	?	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-?^{[verify 3]}	?	Weighted Generations states 2-?^{[verify 3]}	?	?	?	No
Extended Generations	Yes^{[subset 2]}	Yes^{[subset 2]}	No	?	?	?	?	?	?	No
Deficient	Yes^{[subset 2]}	Yes^{[subset 2]}	No	?	?	?	?	?	?	No
Alternating	Yes^{[subset 2]}	rules 2	Yes^{[subset 2]}	?	?	?	?	?	?	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	Yes^{[subset 2]}	Yes^{[subset 2]}	No	?	?	?	?	?	?	No
Deficient	Unclear how deficient rules can generalize to non-isotropic rules
Alternating	Yes^{[subset 2]}	rules 2	No	?	?	?	?	?	?	No

{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^{[subset 6]}	range 1	No	range 1	?	?	range 1	?	?	No
inner	range 1^{[subset 6]}	range 1	No	range 1	?	?	No	?	?	No
outer	range 1^{[subset 6]}	range 1	No	range 1	?	?	No	?	?	No
vertices	range 1^{[subset 6]}	range 1	No	range 1	?	?	No	?	?	No
Moore	range 1-500	range 1-500^{[n 1]}	No	range 1-?	?	?	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	?	?	?	states 2-50	?	?	No
Extended Generations	No	No	No	?	?	?	?	?	?	No
Deficient	No	No	No	?	?	?	?	?	?	No
Alternating	No	rules 2	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	Unclear how deficient rules can generalize to non-isotropic rules
Alternating	No	rules 2	No	?	?	?	?	?	?	No

{4,3,4}

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

2-state

Outer-totalistic

Rulespace	Golly	LifeViewer	lifelib	CAViewer	Caterer	Mirek's Cellebration	Visions of Chaos	Java Cell	Life32	WolframAlpha
von Neumann	range 1^{[emulate 2]}	No	No	?	?	?	range 1	No	?	No
corners	range 1^{[emulate 2]}	No	No	?	?	?	No	No	?	No
edges	range 1^{[emulate 2]}	No	No	?	?	?	No	No	?	No
hexahedral	range 1^{[emulate 2]}	No	No	?	?	?	No	No	?	No
Moore	range 1^{[emulate 2]}	No	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 Cell	Life32	WolframAlpha
Generations	No	No	No	No	No	No	states 2-10	No	No	No

{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 2-10	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 2-10	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

Rulespaces to investigate

The following rulespaces should be investigated to see if they match up with (or can be considered a subset of) existing rulespaces which are not mentioned, or if they are new rulespaces in their own right and can be added as new table rows.

Mirek's Cellebration
- 1D totalistic
- 1D binary
- General binary
- Neumann binary
- Rules tables
- Special rules
- User DLLs
Visions of Chaos
- 1D Cellular Automata
- 1D Cellular Automata 2
- 1D Totalistic Cellular Automata
- Cascade Cellular Automata
- Combinations Cellular Automata
- Extended Neighbourhood Cellular Automata
- Next Nearest Neighbourhood Cellular Auromata
- Traffic Cellular Automata
- Two Steps Back Cellular Automata
- Two Steps Back Extended Cellular Automata
- 2D Totalistic Cellular Automata
- Accretor Cellular Automata
- Alternating Neighbourhoods Cellular Automata
- Alternating Neighbourhoods Cellular Automata 2
- Alternating Neighbourhoods Cyclic Cellular Automata
- Alternating Neighbourhoods Cyclic Cellular Automata 2
- Archean Cellular Automata
- Block Cellular Automata
- Coupled Cellular Automata
- Coupled Cellular Automata 2
- Digital Inkblot
- History Dependent Cellular Automata
- History Dependent Cellular Automata 2
- Hodgepodge Machine
- Indexed Totalistic Cellular Automata
- Indexed Totalistic Cellular Automata 2
- Large Neighbourhood Totalistic Cellular Automata
- Liquid Crystal Cellular Automata
- Majority Rule Cellular Automata
- MergeLife Cellular Automata
- Multiple Neighbourhoods Cellular Automata
- Multiple Neighbourhoods Cellular Automata 2
- Multiple Rules Cellular Automata
- Nonlinear Voter Model
- Pinwheels Cellular Automata
- Rock Paper Scissors Image Cellular Automata
- Sandpile Automata
- Self Replicating Loops
- Smooth Life Cellular Automata
- Stepping Stone Cellular Automata
- Stochastic Cellular Automata
- Tiled Cellular Automata
- Yin Yang Fire Cellular Automata
- Zhang Cellular Automata
- 3D Accretor Cellular Automata
- 3D Cyclic Cellular Automata
- 3D Hexagonal Generations Cellular Automata
- 3D History Dependent Cellular Automata
- 3D Hodgepodge Machine
- 3D Rock Paper Scissors Cellular Automata
- 3D Rule Table Cellular Automata
- 3D Stochastic Cellular Automata
- 3D Voxel Automata Terrain
- 4D Accretor Cellular Automata
- 4D Cyclic Cellular Automata
- 4D Hodgepodge Machine
- 4D Rock Paper Scissors Cellular Automata
Misc.
- "Second-order cellular automata"

Notes

↑ ^1.00 ^1.01 ^1.02 ^1.03 ^1.04 ^1.05 ^1.06 ^1.07 ^1.08 ^1.09 Has a simpler notation for the range-1 case

Emulation via script or custom rule

↑ ^1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 ^1.6 Can be emulated by a multistate ruletable
↑ ^2.0 ^2.1 ^2.2 ^2.3 ^2.4 requires 3D.lua

Emulation via generated rule

↑ ^1.00 ^1.01 ^1.02 ^1.03 ^1.04 ^1.05 ^1.06 ^1.07 ^1.08 ^1.09 Range-1 rules with birth on zero neighbours are emulated accordingly, with black-white reversals for survival on all neighbours or laternating ruels for death on all neighbours
↑ For rules using the general outer-totalistic format, running B0 is only permitted on bounded grids, in which case it is not emulated
↑ Rules where 0000 becomes 1111 and 1111 becomes 0000 are replaced with an alternating rule

Excluded subsets

↑ ^1.0 ^1.1 Odd-numbered rules are not simulated
↑ ^2.00 ^2.01 ^2.02 ^2.03 ^2.04 ^2.05 ^2.06 ^2.07 ^2.08 ^2.09 ^2.10 ^2.11 ^2.12 ^2.13 ^2.14 ^2.15 ^2.16 ^2.17 ^2.18 ^2.19 ^2.20 Cite error: Invalid <ref> tag; no text was provided for refs named bigB0
↑ ^3.0 ^3.1 Consecutive birth/survival transitions (Larger than Life) only for ranges above 2
↑ Consecutive birth/survival transitions (Larger than Life) only for ranges above 5
↑ Rules where 0000 becomes something that is not 0000 are disallowed, except in the case where 0000 becomes 1111 and 1111 becomes 0000 - see next note
↑ ^6.0 ^6.1 ^6.2 ^6.3 ^6.4 ^6.5 B0 is completely disallowed for the conventional range-1 format
↑ ^7.0 ^7.1 ^7.2 ^7.3 Only range-1 Moore natively supported, and range-1 von Neumann through its notation
↑ All rules involved must use the same neighbourhood and be in the same rule family
↑ Excluding Margolus

As subsets

↑ ^1.0 ^1.1 ^1.2 ^1.3 As a subset of elementary Wolfram CA
↑ ^2.00 ^2.01 ^2.02 ^2.03 ^2.04 ^2.05 ^2.06 ^2.07 ^2.08 ^2.09 ^2.10 ^2.11 ^2.12 ^2.13 ^2.14 ^2.15 ^2.16 ^2.17 ^2.18 ^2.19 ^2.20 ^2.21 ^2.22 ^2.23 ^2.24 ^2.25 ^2.26 ^2.27 ^2.28 ^2.29 ^2.30 ^2.31 ^2.32 ^2.33 ^2.34 ^2.35 ^2.36 ^2.37 ^2.38 ^2.39 ^2.40 ^2.41 ^2.42 ^2.43 ^2.44 ^2.45 ^2.46 ^2.47 Requires custom ruletables
↑ ^3.0 ^3.1 ^3.2 ^3.3 ^3.4 via Moore isotropic non-totalistic notation
↑ ^4.00 ^4.01 ^4.02 ^4.03 ^4.04 ^4.05 ^4.06 ^4.07 ^4.08 ^4.09 ^4.10 ^4.11 For Java Cell applications, neighbourhoods are manually specified and not systematically generated
↑ ^5.00 ^5.01 ^5.02 ^5.03 ^5.04 ^5.05 ^5.06 ^5.07 ^5.08 ^5.09 ^5.10 via Weighted Life
↑ ^6.0 ^6.1 ^6.2 ^6.3 Requires the use of a custom CoordCA neighbourhood

Needs verification

↑ ^1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 Possibly as a subset of other supported 1D rulespaces
↑ ^2.0 ^2.1 ^2.2 ^2.3 ^2.4 ^2.5 ^2.6 ^2.7 "Large Neighborhood Totalistic Cellular Automata" may allow for this - testing needed
↑ ^3.00 ^3.01 ^3.02 ^3.03 ^3.04 ^3.05 ^3.06 ^3.07 ^3.08 ^3.09 ^3.10 ^3.11 Extended neighbourhoods unknown

[r1notation-5] 1.00 ^1.01 ^1.02 ^1.03 ^1.04 ^1.05 ^1.06 ^1.07 ^1.08 ^1.09 Has a simpler notation for the range-1 case

[emulate-15] 1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 ^1.6 Can be emulated by a multistate ruletable

[3Dscript-24] 2.0 ^2.1 ^2.2 ^2.3 ^2.4 requires 3D.lua

[B0-6] 1.00 ^1.01 ^1.02 ^1.03 ^1.04 ^1.05 ^1.06 ^1.07 ^1.08 ^1.09 Range-1 rules with birth on zero neighbours are emulated accordingly, with black-white reversals for survival on all neighbours or laternating ruels for death on all neighbours

[bigB0-7] For rules using the general outer-totalistic format, running B0 is only permitted on bounded grids, in which case it is not emulated

[margolus-17] Rules where 0000 becomes 1111 and 1111 becomes 0000 are replaced with an alternating rule

[odd1D-3] 1.0 ^1.1 Odd-numbered rules are not simulated

[bigB0-8] 2.00 ^2.01 ^2.02 ^2.03 ^2.04 ^2.05 ^2.06 ^2.07 ^2.08 ^2.09 ^2.10 ^2.11 ^2.12 ^2.13 ^2.14 ^2.15 ^2.16 ^2.17 ^2.18 ^2.19 ^2.20 Cite error: Invalid <ref> tag; no text was provided for refs named bigB0

[oldltl-10] 3.0 ^3.1 Consecutive birth/survival transitions (Larger than Life) only for ranges above 2

[ctgltl-13] Consecutive birth/survival transitions (Larger than Life) only for ranges above 5

[margolus-16] Rules where 0000 becomes something that is not 0000 are disallowed, except in the case where 0000 becomes 1111 and 1111 becomes 0000 - see next note

[noB0gen-18] 6.0 ^6.1 ^6.2 ^6.3 ^6.4 ^6.5 B0 is completely disallowed for the conventional range-1 format

[lowext-20] 7.0 ^7.1 ^7.2 ^7.3 Only range-1 Moore natively supported, and range-1 von Neumann through its notation

[neighbourhood-21] All rules involved must use the same neighbourhood and be in the same rule family

[nomarg-22] Excluding Margolus

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

[ruletable-4] 2.00 ^2.01 ^2.02 ^2.03 ^2.04 ^2.05 ^2.06 ^2.07 ^2.08 ^2.09 ^2.10 ^2.11 ^2.12 ^2.13 ^2.14 ^2.15 ^2.16 ^2.17 ^2.18 ^2.19 ^2.20 ^2.21 ^2.22 ^2.23 ^2.24 ^2.25 ^2.26 ^2.27 ^2.28 ^2.29 ^2.30 ^2.31 ^2.32 ^2.33 ^2.34 ^2.35 ^2.36 ^2.37 ^2.38 ^2.39 ^2.40 ^2.41 ^2.42 ^2.43 ^2.44 ^2.45 ^2.46 ^2.47 Requires custom ruletables

[mooresubset-9] 3.0 ^3.1 ^3.2 ^3.3 ^3.4 via Moore isotropic non-totalistic notation

[specify-12] 4.00 ^4.01 ^4.02 ^4.03 ^4.04 ^4.05 ^4.06 ^4.07 ^4.08 ^4.09 ^4.10 ^4.11 For Java Cell applications, neighbourhoods are manually specified and not systematically generated

[weightedsubset-14] 5.00 ^5.01 ^5.02 ^5.03 ^5.04 ^5.05 ^5.06 ^5.07 ^5.08 ^5.09 ^5.10 via Weighted Life

[customnotation-23] 6.0 ^6.1 ^6.2 ^6.3 Requires the use of a custom CoordCA neighbourhood

[poss1Dsubset-2] 1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 Possibly as a subset of other supported 1D rulespaces

[possiblehrot-11] 2.0 ^2.1 ^2.2 ^2.3 ^2.4 ^2.5 ^2.6 ^2.7 "Large Neighborhood Totalistic Cellular Automata" may allow for this - testing needed

[unkext-19] 3.00 ^3.01 ^3.02 ^3.03 ^3.04 ^3.05 ^3.06 ^3.07 ^3.08 ^3.09 ^3.10 ^3.11 Extended neighbourhoods unknown

[subset 1]

[verify 1]

[exclude 1]

[subset 2]

[n 1]

[equivalent 1]

[equivalent 2]

[exclude 2]

[subset 3]

[exclude 3]

[verify 2]

[subset 4]

[exclude 4]

[subset 5]

[emulate 1]

[exclude 5]

[equivalent 3]

[exclude 6]

[verify 3]

[exclude 7]

[exclude 8]

[exclude 9]

[subset 6]

[emulate 2]

Cellular automaton simulation programs by supported rulespaces

Grids

Euclidean regular

{∞}

2-state

Outer-totalistic

Isotropic non-totalistic

Non-isotropic

n-state

Outer-totalistic

Isotropic non-totalistic

Non-isotropic

{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}

2-state

Outer-totalistic

n-state extensions of 2-state

Outer-totalistic

{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

Rulespaces to investigate

Notes

Emulation via script or custom rule

Emulation via generated rule

Excluded subsets

As subsets

Needs verification

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