Cellular Automata rules lexicon

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Family: Neumann binary

Type: binary, 2 bit, in von Neumann neighborhood

Neumann binary family of rules allows defining binary (configuration-specific) rules in Neumann neighborhood. MCell's implementation allows defining rules with up to 4 states of cells.

Neumann binary rules notation

Neumann binary rules are represented as a string of digits. The first digit specifies the count of states, 2, 3, or 4; the rest of digits define the transition table - the state a cell will have in every possible configuration. For enumerating all possible neighborhood configurations the "ME,N,E,S,W" order is used.

Example:
Fredkin2 rule has the following definition: 201101001100101101001011001101001
The first digit, '2', tells the rule has 2 states (it's a 1 bit rule).
The second digit, '0', tells a cell in a configuration ME=0,N=0,E=0,S=0,W=0 will get the state 0.
The third digit, '1', tells a cell in a configuration ME=0,N=0,E=0,S=0,W=1 will get the state 1.
The fourth digit, '1', tells a cell in a configuration ME=0,N=0,E=0,S=1,W=0 will get the state 1.
The fifth digit, '0', tells a cell in a configuration ME=0,N=0,E=0,S=1,W=1 will get the state 0.
. . .

Note!
Neumann totalistic rules are much easier to define in "Weighted Life" family.

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

MCell built-in Neumann binary rules

Name Character Rule Description
Aggregation Chaotic
A special type of crystallization that looks like aggregation. It features a dramatic "phase transition" from "fluid" semi-spiral dynamics to a "solid" aggregate crystal. The rule uses 3 states.
A rule by Tomoaki Suzudo, 2000.
Birds Chaotic
'Aquarium' family member. The rule shows self-organization resembling traveling birds.
A rule by Tomoaki Suzudo, August 1999.
Colony Chaotic
"In 'Colony', static marks spread all over the space as the time goes. This process looks like a sort of colonization." - T.S.
A rule by Tomoaki Suzudo, June 2000.
Crystal2 Chaotic
This is the simplest (2-state) example of self-organization at the edge of chaos. The crystallization appears at the critical point between organized and chaotic areas.
A rule by Tomoaki Suzudo, 1999.
Crystal3a Chaotic
Another crystallization effect. The rule uses 3 states.
A rule by Tomoaki Suzudo, 1999.
Crystal3b Chaotic
Another crystallization effect. The rule uses 3 states.
A rule by Tomoaki Suzudo, 1999.
Fredkin2 Exploding
Famous Fredkin's replicator in von Neumann neighbourhood. This is the simple rule which makes patterns self replicate. After 32 steps every starting pattern is replicated 5 times.
A rule by Edward Fredkin, 1999.
Fredkin3 Exploding
Another version of Fredkin's replicator in von Neumann neighbourhood. This version uses 3 states. After 27 steps every starting pattern is replicated 5 times.
A rule by Edward Fredkin, 1999.
Galaxy Chaotic
"Similar to Typhoon, but the growth of the vortex is limited, and sometimes it collapses. In Galaxy, any [2-cells] can not survive when at least one of the neighbors is [a 2-cell]. This is added to Typhoon's rule." - T.S.
A rule by Tomoaki Suzudo, 2000.
Greenberg Expanding
A simple rule which sends out walls of 2 cell thicknesses in all 4 directions, the overall shape of which being that of  the shortest path around the original pattern. Compare also "GreenHast" rule in "User DLLs" family.
A rule by J. Greenberg. Coded in MCell by Charles A Rockafellor.
Honeycomb Chaotic
"In 'Honeycomb', crystalline and dynamic parts coexist. Such combination is essential to various complex system. For instance, organism is composed of static structures communicating one another." - T.S.
A rule by Tomoaki Suzudo, June 2000.
Knitting Chaotic
A rule by Tomoaki Suzudo, June 2000.
Lake Chaotic
'Aquarium' family member. The rule adds some chaos to the Pond rule.
A rule by Tomoaki Suzudo, 1999.
Plankton Chaotic
'Aquarium' family member. The rule produces little creatures like in Pond, their movement looks like plankton.
A rule by Tomoaki Suzudo, 1999.
Pond Chaotic
The main 'Aquarium' family member. This beautiful rule produces hordes of various little creatures crawling in the pond.
A rule by Tomoaki Suzudo, 1999.
Strata Gliding
This rule goes through phases of layer forming, stability, and slow decay.
A rule by Ben Schaeffer, 2000.
Tanks Chaotic
A rule by Tomoaki Suzudo, 1999.
Typhoon Chaotic
'Aquarium' family member with  an interesting "phase transition". Apparently similar to Lake, the rule very often produces stable spiral cores that slowly take over the lattice swallowing all little creatures.
A rule by Tomoaki Suzudo, 1999.
Wave Chaotic
"'Wave causes quasi-static waves which are more likely to appear in nature than purely static ones." - T.S.
A rule by Tomoaki Suzudo, June 2000.

 


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Last update: 15 Sep 2001