Cellular Automata rules lexicon

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Family: 1D binary CA

Type: 1-D binary with optional decay

This game allows exploring a very wide range of popular one-dimensional binary Cellular Automata. Most of included rules come from an excellent collection of Martin Schaller. You should also check Martin's 1-D binary rules browser.

The unique feature of MCell's implementation of one-dimensional binary CA is History. Like in "Generations" family, when history in on, cells that would simply die are getting older, up to the maximum specified state. Such cells cannot give birth to new cells, but they occupy the space of the lattice, thus changing the rules radically.

The user interface of the game allows specifying rules for calculating next rows of cells. The neighborhood can be defined in a range 1-4, allowing up to 9 cells to be considered. Rules specify the state of new cells for each possible configuration of existing cells found in the defined neighborhood.

The lattice can be treated as a ring. When board wrapping is on, active cells that leave at the right edge enter again on the left edge and vice versa. Note that randomizing the board fills only the top row of one-dimensional universe. All patterns are loaded at the top of the lattice, too. One can use all drawing tools available in the program, but only cells in the active row are taken into account. At the beginning the active row is the top row. After animating the rule the active top moves down.

One-dimensional binary CA notation
The notation of one-dimensional totalistic CA rules has the "R,W,H" form, where:
R   specifies the range (1..4) of the neighborhood.
W  specifies the Wolfram's code of the rule, expressed as a hexadecimal value. Wolfram's code is a compact way of specifying the complete 1-D binary rules table.
H - specifies the count of states, 0..25. Parameter 'H' is optional. No parameter or a value smaller than 3 means the history is not active. Values greater than 2 activate the history, with the given count of states.

Sample rule in R1 neighborhood (3 cells: left, center, and right):

111 110 101 100 011 010 001 000 <= all possible configurations
0 1 1 0 1 1 1 0 <= the rule

The rule can be expressed as a binary number 01101110, what is 6E in hexadecimal notation. Finally the rule in MCell's notation has the form "R1,W6E"

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

MCell built-in 1-D totalistic CA rules

Name Rule (R,W) Description
Bermuda Triangle R2,WBC82271C  
Brownian motion R1,W36 Rule 54
Chaotic gliders R2,WAD9C7232  
Compound glider R2,W89ED7106  
Filiform gliders 1 R2,W1C2A4798  
Filiform gliders 2 R2,W5C6A4D98  
Fish-bones R2,W5F0C9AD8  
Fishing-net R1,W6E Rule 110
Glider p106 R2,WB51E9CE8  
Glider-gun p168 R2,W6C1E53A8  
Heavy triangles R1,W16 Rule 22
Inverse gliders R2,W360A96F9  
Kites R2,WBF8A5CD8  
Linear A R1,W5A Rule 90
Linear B R1,W96 Rule 150
Pascal's Triangle R1,W12 Rule 18
Plaitwork R2,W6EA8CD14  
R3 Gliders R3,W3B469C0EE4F7FA96 F93B4D32B09ED0E0  
Raindrops R2,W4668ED14  
Randomizer 1 R1,W1E Rule 30
Randomizer 2 R1,W2D Rule 45
Relief gliders R2,WD28F022C  
Scaffolding R2,W6EEAED14  
Solitons A R2,WBF8A18C8  
Solitons A' R2,WBF8A58C8  
Solitons B R2,W3CC66B84  
Solitons B' R2,W3EEE6B84  
Solitons B3 R2,W1D041AC8  
Solitons C1 R2,W5F2A9CC8  
Solitons C2 R2,W1D265EC8  
Solitons D1 R2,W2F8A1858  
Solitons D2 R2,W1D065AD8  
Solitons E R2,WBDA258C8  
Solitons F R2,W9D041AC8  
Stable gliders R2,W7E8696DE  
Threads R2,W978ECEE4  
Triangular gliders R2,WE0897801  
Zig-Zags R2,W8F0C1A48  


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Last update: 10 Mar 2002