Cellular Automata rules lexicon
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
Note that the count of colors (states) has no influence on next generations, because Life is a one-bit family of rules.
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.
|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.
|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.
|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.
|Assimilation||4567/345||Stable||Rule similar to Diamoeba, but much more stable. The diamond-shaped
patterns are filled in 70-85% and never die.
|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.
|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.
|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.
|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.
|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.
|Replicator||1357/1357||Exploding||In this remarkable universe every pattern is a replicator. After 32 steps
every starting pattern is replicated 8 times.
|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
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.
|Stains||235678/3678||Stable||Most close variations of these rules expand forever, but this one
curiously does not. Why?
|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
A rule by David Macfarlane.
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Last update: 15 Sep 2001