Cellular Automata rules lexicon

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Family: Life

Type: outer totalistic, 1 bit

"Life" rules family allows to play the widest-known Cellular Automata, including the mythical Conway's Life.

MCell contains many built-in "Life" rules. Many of them come from an excellent 32-bit Windows Life program - Life32 by Johan Bontes. They were collected and described by Alan Hensel, an author of the fastest Java applet running Conway's Life patterns.
Note that the count of colors (states) has no influence on next generations, because Life is a one-bit family of rules.

Life rules notation

Life rules are defined in the "S/B" form, where:
S - defines counts of alive neighbors necessary for a cell to survive,
B - defines counts of alive neighbors necessary for a cell to be born.

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

MCell built-in Life rules

Name Rule (S/B) Character Description
2x2 125/36 Chaotic Similar in character to Conway's Life, but creates completely different patterns. Many different oscillators occur at random, and a rare glider. Simple block seeds usually lead to oscillators of various periods.
This rule is also a 2x2 block universe. This means that patterns consisting entirely of 2x2 blocks, all aligned, will continue to consist of 2x2 blocks.
Author unknown.
34 Life 34/34 Exploding One of the first explored alternatives to Conway's Life, back in the early 1970's. Computing power was so low back then, it was months before anyone noticed that this is an exploding universe. What makes this universe interesting is the variety of small oscillators and the period-3 orthogonal spaceship.
Author unknown.
Amoeba 1358/357 Chaotic An "amoeba" universe - forms large random areas that resemble amoebas. Internal to a random area is chaos. The edge vacillates wildly, and patterns tend to grow more than shrink. The more they grow, the more certain their survival. This is a fairly well-balanced rule.
Author unknown.
Assimilation 4567/345 Stable Rule similar to Diamoeba, but much more stable. The diamond-shaped patterns are filled in 70-85% and never die.
Author unknown.
Coagulations 235678/378 Exploding Creates gooey coagulations as it expands forever. Best viewed at zoom=1. Notice that this is a close variation of the previous rule, 235678/3678, except that there is one less condition for a dead cell to come to life on the next generation. In general this should make a universe less active, but this is an exception.
Author unknown.
Conway's Life 23/3 Chaotic This is the most famous cellular automata ever invented. People have been discovering patterns for this rule since around 1970. Large collections are available on the Internet.
The rule definition is very simple: a living cell remains alive only when surrounded by 2 or 3 living neighbors,  otherwise it dies of loneliness or overcrowding. A dead cell comes to life when it has exactly 3 living neighbors.
A rule by John Conway.
Coral 45678/3 Exploding This rule produces patterns with a surprisingly slow rate of expansion and an interesting coral-like texture.
Author unknown.
Day & Night 34678/3678 Stable So named because dead cells in fields of live cells act by the same rules as live cells in fields of dead cells. There are obviously other rules, which have this symmetrical property, but this rule was chosen because it has some interesting high period spaceships and oscillators. The properties of the rule were explored by David Bell.
A rule by Nathan Thompson.
Diamoeba 5678/35678 Chaotic Creates solid diamond-shaped "amoeba" patterns that are surprisingly unpredictable. For a long time it was not known whether any diamonds expand forever, or if the tendency toward the catastrophic destruction of corners is too strong. Finally in March 1999 David Eppstein found the  c/7 spaceship, and David Bell made a 100% spacefiller out of it.
A rule by Dean Hickerson.
Flakes 012345678/3 Expanding Also known as Life without Death (LwoD).
The rule produces beautiful flakes, starting from simple groups of cells. Try for example various filled circles with radius > 20 cells. The rule produces also ladders, what allowed David Griffeath and Cris Moore to prove that the rule is P-complete.
A rule by Janko Gravner.
Gnarl 1/1 Exploding A simple rule provided by Kellie Evans. To see its beauty start with simple patterns, for example with a single dot.
HighLife 23/36 Chaotic This rule is very similar to Conway's Life, but it has a surprise replicator pattern. There is no known replicator in Conway's Life.
A rule by Nathan Thompson.
InverseLife 34678/0123478/2 Chaotic The rule shows similar oscillators and gliders to GOL, but dead cells create the patterns amongst live cells in the background.
A rule by Jason Rampe.
Long life 5/345 Stable This rule is called "Long life" because of the extremely high period patterns that can be produced in this universe.
A rule by Andrew Trevorrow.
Maze 12345/3 Exploding An "a-maze-ing" universe - crystallizes into maze-like patterns. Interesting variations: try removing 5 from the "Survival" list. To produce mice running in the maze, add 7 to the "Births" list.
Author unknown.
Mazectric 1234/3 Exploding "Mazectric" and "Corrosion of Conformity". An interesting variation of the Maze rule which produces longer halls and a highly linear format. Adding B7 to maze (keeping S5) allows some "mice" to run back and forth in the halls. Switching the B3 to B45 though, electrifies the mazes. Dropping S3 gives "Corrosion of Conformity", a slow burn from almost any starting pattern, resulting in a rusting away of the local continuum.
A rule by Charles A. Rockafellor.
Move 245/368 Stable A very calm universe, which nonetheless has a very commonly occurring slow spaceship and a slow puffer.
Author unknown.
Pseudo life 238/357 Chaotic In this close variation of Conway's Life, the chaos is remarkably similar, but almost none of the engineered patterns work.
Author unknown.
Replicator 1357/1357 Exploding In this remarkable universe every pattern is a replicator. After 32 steps every starting pattern is replicated 8 times.
Author unknown.
Seeds (2) /2 Exploding Every living cell dies every generation, but most patterns explode anyway. It's a challenge to build new patterns that don't explode. Arguably the simplest challenging rule.
A rule by Brian Silverman.
Serviettes /234 Exploding Like /2, every living cell dies every generation. This rule is picked for the exceptional fabric-like beauty of the patterns that it produces.
Author unknown.
Stains 235678/3678 Stable Most close variations of these rules expand forever, but this one curiously does not. Why?
Author unknown.
WalledCities 2345/45678 Stable The rule creates walled cities of activity. Once the field has stabilized, one can draw lines to connect the cities and the patterns expand to create an even larger city. But once the wall is complete, the city never grows, even though there is near-random activity inside it.
A rule by David Macfarlane.


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Last update: 15 Sep 2001