Cellular Automata rules lexicon

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Family: General binary

Type: 2D, binary, in Moore and von Neumann neighborhood, with optional decay

General binary family allows defining a wide range of rules in both Moore and von Neumann neighborhood. In contrast to totalistic CA, General binary rules distinguish not only the count of neighboring cells, but also their location, thus allowing for defining anisotropic (configuration-specific) rules.

General binary rules notation

The notation of General binary rules has the "C/N/S/B" form, where:
C - specifies the count of states in the rule (0..C-1).
N - specifies the neighborhood type: NM stands for Moore, NN for von Neumann.
S - specifies the compressed string defining the configurations where a cell survives.
B - specifies the compressed string defining the configurations where a cell is born.

Strings defining S and B parts specify the 0/1 state for every possible configuration. For enumerating all possible neighborhood configurations the "N,NE,E,SE,S,SW,W,NW" order is used. For example S010000...0 means "Survival on an alive N neighbor", B1100...0 means "Birth on no neighbors or on a single N neighbor". To make the S/B strings shorter a simple compression is used. 0s are represented as "a", 1s as "b". 3 and more occurrences of the same character are shortened by specifying the count of occurrences and a character.

"Fallski" rule is defined as follows: "C48,NM,Sb255a,Babb189ab63a".
It has 48 states (0..37) and uses the Moore neighborhood. "Sb255a" means 1 and 255 0s (survival only on no alive neighbors). "Babb189ab63a" means 0,1,1, 189 0s, 1, 63 0s (birth on a single N or  NE neighbor, or on W and NW neighbors).

All rules from Life, Generations, Vote, and Weighted Life families can be also represented as General binary rules. MCell's General binary rules designer allows for automatic importing and translation of such rules.

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

MCell built-in General binary rules

Name Character Rule Description
Banks Stable
Banks rule, also known as "Banks' Computer", has been proven to be ideal for constructing the logic elements of a virtual computer. The rule discriminates between neighbor configurations. If a 1-cell has exactly two neighbors, and if these neighbors are adjacent to one another rather than opposite one another, the cell goes to 0. A 0-cell with more than two neighbors goes to 1. In all other cases, the cell remains unchanged.
A rule by Edwin Banks.
Fallski Expanding
"The rule draws a skewed Sierpinski gasket that gradually fades out. The visual effect reminded me of falling leaves, hence the name. The cellsize (count of states) of 48 is arbitrary, having been set to match the universe height of a particular seed." - J.E.
A rule by John Elliott, June 1998.
FractalBeads Exploding
"This CA belongs to a large family of what we might call "Sierpinski rules", in virtue of the fact that they produce structures closely related to the so-called Sierpinski gasket, a well-known classical fractal.
This particular rule propagates in the NW direction, but naturally each of its three rotations propagates in a different corner direction. The considerable transmusical interest of this and other Sierpinski rules has been the occasion for my dabbling with them." - J.E.
A rule by John Elliott.
JustFriends Chaotic
The rule is called "Just Friends" because new cells are born from a pair of parents, but not from ones which are "too intimate" with each other. A cell stays alive only if it has 1 or 2 live neighbors (in any position). A cell is born only if it has exactly two live neighbors which are not adjacent vertically or horizontally.
The rule has two small period 6 diagonal gliders, an interesting period 236 cyclic oscillator, and a small c/3 orthogonal wickstretcher which show up from random soups. Lines of cells are stable. Random soups tend to quickly settle down into small clumps of lines. But there are lots of spaceships, wickstretchers, rakes, and glider guns which have been built.
A rule by David I. Bell
LogicRule Chaotic
A two-state configuration-specific cellular automata with gliders that move orthagonally one cell per generation - the speed of light. The glider guns, called "Bit Stream Generators", can be built to output a huge selection of seemingly random bits. The BSG's can be positioned so that collisions between glider streams can easily demonstrate logic gates.
A rule by David Conant, March 2001.
Meteorama Gliding
"This is a randomly-generated rule. As such it is suggestive only - the table needs to be simplified. But the bidirectional meteor shower theme seems worth exploring, and also the orbits were found to produce compelling transmusic." - J.E.
A rule by John Elliott, April 1996
Sierpinski Expanding
A simple Sierpinski gasket drawer. A dead cell comes to life if it has a single living neighbor that is either its W or S neighbor. In all other cases, it stays dead. All living cells survive. Seeded with a single cell the rule produces the Pascal's triangle, but... rotated 45°.
Author unknown.
Slugfest Chaotic
"This is a randomly-generated rule. As such it is suggestive only - the table needs to be simplified. But who can resist the enchanting theme of slug-like gliders that lay down slime trials." - J.E.
A rule by John Elliott, March 1996
Snowflakes Chaotic
An anisotropic rule. One of the most common objects is a falling 'snowflake'. Not everything is forced downwards however; a rocket takes off at c/2!
A rule by Chris Gordon-Smith, January 1997.
Coded in MCell by Charles A. Rockafeller, October 2000.
Springski Expanding
A simple Moore Sierpinski gasket tracer.
A rule by John Elliott.


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Last update: 15 Sep 2001