List of isotropic non-totalistic rules

The following is a list of isotropic non-totalistic rules. A more up-to-date and complete list can be found on Catagolue.

Non-totalistic rules

See also: Non-totalistic cellular automaton, Hensel notation

Rulestring	Name	Description
B1e2cn3acjkr4cny5einqy6ei7c/S01e2-ei3acjkr4-ejr5einqy6-cn7c8		Checkerboard dual of Day & Night
B2-a/S12	Just Friends	One of the first isotropic non-totalistic cellular automata considered. It normally stabilizes into a maze-like structure consisting of lines and oscillators with escaping 3-cell spaceships.
B2-an3acqry4cnw5-cj6cei78/S1c2n3-nqy4acknqtw5-ijkr6ei78		Rule that contains a c/5953 elementary spaceship, the slowest known in a two-state isotropic rule.
B2ae/S	Logic Rule	One of the early demonstrations showing how signal circuitry can be built in simple cellular automata. The domino is a replicator, also contains c orthogonal ships and puffers.
B2c3ae4ai56c/S2-kn3-enq4		Allows for arbitrary spaceships speeds of c/n where n is an even number and greater than 3.
B2c3aj4nrt5i6c78/S1c23enr4aet5-iq67		Allows for arbitrary spaceships speeds of c/n where n is an odd number and greater than 4.
B2ikn3-ejnq4knqt5cjnry6in/S01e2aen3-aeq4ceikty5-c6-ak78		Rule that contains a c/1860 diagonal elementary spaceship, the slowest known in a two-state isotropic rule.
B2in3/S123a	Goat Flock	Resembles Flock and 2x2, although it takes a lot longer to settle. Goat Flock oscillators tend to have very high periods. There is also a natural 2c/7 orthogonal spaceship.
B2i3/S23	B2i3/S23	Honeyfarm predecessors from Life evolve instead into a p20 oscillator in this rule.
B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e	Snowflakes	A rule named after a common still life known as a snowflake, with much engineering potential.
B2i34c/S2-i3	Salad	Also has multiple small spaceships.
B2n3/S23-q	LeapLife	Differs from Conway's Game of Life by two transitions, much like tlife, but is much more stable.
B2n36/S23-q	HighLeapLife	Similar to LeapLife, also has a common p96 RRO and a p72 oscillator, which was discovered in D4_+1.
B2n37/S23-q	DryLeapLife	Similar to LeapLife, with a natural c/7o and a gliderless c/4d, the latter of which was found in D8_1.
B2n3/S23-q4e8	LispLife	More active variant of LeapLife. A natural p122 oscillator has been discovered.
B2n37/S2-i3-q4q	tDryLeapLife	Variant of LeapLife that has the glider, the c/5 orthogonal T, and an unnamed 3c/27o.
B3-jknr4ity5ijk6i8/S23-a4city6c7c	Glimmering Garden	An active rule with several high-volatility oscillators, one of which can be shifted by t-ships to form a family of adjustable-slope oblique ships.
B3-n4nt5qr6i/S23	FattyLife	A rule which is specifically tailored to support the overweight spaceship with spark length 3
B3/S2-ak34aikqtwz5inqy	Conway+-
B3/S2-ei3	Conway--	A Life variation which subtracts the survival rule of 2 orthogonal neighbors, the result being that everything dies down quickly.
B3/S23-inqy4aikqtwz	Conway+-1	A distant Life variation, commonly features a zigzag puffer train.
B3/S2-i34q	tlife	T-tetromino is a common c/5 orthogonal spaceship in this rule, giving it its name. Possibly the best-explored 2-dimensional 2-state non-totalistic cellular automaton.
B3/S234c	Conway++	A Life variation which adds the survival rule of 4 diagonal neighbors, the result being that chaotic expansion is extended.
B3/S234z	Zlife	A rule where the Z-pentomino is stable, supports a 8c/16 ship, a p58 flipper, and a rephased 55p9 middleweight sparker based on life's 55p10. While Snark fails here, Snark64 works to provide several adjustable alien guns.
B34c/S23	4diagonal	A Life variation which adds the birth rule of 4 diagonal neighbors, has a 46c/220 dirty puffer based on the century.
B34c/S234c		A rule which combines 4diagonal and Conway++, retaining several patterns from both rules.
B34ek5ak/S2-c34z	GlideLife	GlideLife is an isotropic non-totalistic Life-like cellular automaton with many small elementary spaceships.
B34w/S23	Wlife	Wlife is an explosive rule because the t-tetromino is a 2c/5 failed replicator.
B36/S2-i34q	tHighLife	Has an orthogonal replicator sharing some traits with HighLife's diagonal replicator. A cross between tlife and HighLife.
B367/S2-i34q	SilverLife	A rule extremely rich in exotic speeds, including a p91 flamingoship.
B36n/S23	Ship	One of the first isotropic non-totalistic cellular automata considered. The name was chosen due to the 6n configuration resembling a ship, and the rule itself is notable for being the closest isotropic rule to Life to feature HighLife's Replicator.
B37/S2-i34q	tDryLife	Not explosive, unlike DryLife. Has a small 2c/23 orthogonal, a high-period diagonal pond puffer, and a ship camelpuffer, both of which have been stabilised. A cross between tlife and DryLife.
B37e/S23	PiLife	A variant of DryLife which is of interest because it supports several aspects of DryLife while being stable. There is also a 11c/52 puffer and spaceship.

See also

• List of Life-like rules
• List of strobing rules
• List of Generations rules