List of isotropic non-totalistic rules

See also: Non-totalistic cellular automaton, Hensel notation

The following is a brief list of some of the more notable isotropic non-totalistic rules, including many of the first to be explored. A more up-to-date and complete list can be found on Catagolue.

Rulestring	Name	Description
B1e2cn3acjkr4cny5einqy6ei7c/S01e2-ei3acjkr4-ejr5einqy6-cn7c8		Checkerboard dual of Day & Night - simulates Day & Night if the entire plane was tiled with a checkerboard pattern of off/on cells.
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-ak3ce4eikqrz5-iknq6-ek8/S1c2aek3aekn4eiknry5eiky6-ei7c8		Rule with over 1000 Non-Reducible Spaceship Speeds (NRSS), the most of any rule.
B2-an3acqry4cnw5-cj6cei78/S1c2n3-nqy4acknqtw5-ijkr6ei78		Rule that contains a c/5953 elementary spaceship. At the time of discovery, that spaceship was 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. There are c orthogonal spaceships and puffers, and the domino is a replicator.
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.
B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e	Snowflakes	A rule named after a common still life known as a snowflake, with much engineering potential.
B2i3/S23	B2i3/S23	A 1tfl rule commonly known as HoneyBomb life. Honeyfarm predecessors from Life evolve instead into a p20 oscillator in this rule.
B2i34c/S2-i3	Salad	Also has multiple small spaceships.
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.
B2n3/S23-q	LeapLife	Differs from Conway's Game of Life by two transitions (2tfl), much like tlife, but is much more stable.
B2n3/S23-q4e8	LispLife	More active variant of LeapLife. A natural p122 oscillator has been discovered.
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.
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 egg length 3.
B3-q/S23	qlife	A rule which differs from Life by the lack of the B3q transition. Patterns generally tend to create denser remnants compared to Life, along with taking somewhat less time to stabilise.
B3/S2-ak34aikqtwz5inqy	Conway+-
B3/S2-ei3	Conway--	A 2TfL Life variation where cells with 2 orthogonal neighbors die, the result being that everything dies down quickly.
B3/S23-a5	Travelling Ts	An isotropic non-totalistic cellular automaton named in reference to its most common spaceship, known as the T.
B3/S23-inqy4aikqtwz	Conway+-1	A distant Life variation, commonly features a zigzag puffer train.
B3/S2-i34q	tlife	A rule 2 transitions from life (2TFL ). T-tetromino is a common c/5 orthogonal spaceship in this rule, giving it its name. Possibly the best-explored 2-dimensional 2-state isotropic non-totalistic cellular automaton.
B3/S234c	Conway++	A rule 1 transition from Life (1TFL) which, according to measurements of the frequency of range-1 moore transitions queried by random soups, is the rule most similar to B3/S23 among all range-1 isotropic non-totalistic rules. In terms of differences, there is an alien p62, diamond checkerboard agars are stable and infinitely extensible in two dimensions, and both the switch engine and the century (among others) fail.
B34c/S23	4diagonal	a 1TFL rule with two small elementary c/17 orthogonal ships, a larger corderized 17c/35 orthogonal ship, and a century-based 46c/220 orthogonal puffer. Most notable for being proven Omniperiodic before B3/S23.
B34k/S23	4K Life
B34ek5ak/S2-c34z	GlideLife	GlideLife is an isotropic non-totalistic Life-like cellular automaton with many small elementary spaceships.
B34w/S23	Wlife	An 1TFL rule which is explosive because the t-tetromino is a 2c/5 failed replicator.
B35y/S23	hatlife	Rule named after the fact that the Hat is a c/3 spaceship.
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 tlife variant notable for a couple exotic speeds, including a p91 flamingoship.
B36n/S23	Ship	One of the first isotropic non-totalistic cellular automata considered, also 1TFL. The name was chosen due to the 6n configuration resembling a ship (which itself is no longer stable), and the rule itself is notable for being the closest isotropic rule to Life to feature a variant of HighLife's Replicator.
B37/S2-i34q	tDryLife	Cross between tlife and DryLife which, unlike the latter, is not explosive. 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.
B37c/S23	B37c/S23	An explosive rule with the spinner from 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.
B37e/S238	B37e/S238	An almost explosive variant of PiLife with S8 added, causing it to inherit patterns from EightLife. This rule has a natural period-10 oscillator and a (21,6)c/177 puffer.

See also

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