Cellular Automata rules lexicon

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):

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

Webmaster: Mirek Wojtowicz http://www.mirekw.com

MCell mirrors: USA  http://psoup.math.wisc.edu/mcell/ Europe  http://www.mirwoj.opus.chelm.pl

Last update: 10 Mar 2002