Basic Rule Notation

Rule notation is based upon traditional "birth/survive" rule notation. The characters "a" to "e" are used to indicate the number of side neighbors in the rule. "a" corresponds to zero side neighbors, while "e" corresponds to four side neighbors. Here are the meaningful combinations of total and side counts: 

     0a
     1ab
     2abc
     3abcd
     4abcde
     5bcde
     6cde
     7de
     8e

Here is the full rule specification for Game Of Life: 

     3abcd/2abc3abcd

If a total count is specified without side counts it is equivalent to all meaningful side counts having been specified. Each of the following specifies Game Of Life: 

     3abcd/2abc3
     3abcd/23abcd
     3abcd/23
     3/2abc3abcd
     3/2abc3
     3/23abcd
     3/23

Colors

The color used to display a live cell is dependent upon:
  • the cell's total neighbor count
  • the cell's side neighbor count
  • the color the cell was born with if the cell is a survivor.

    Color Game Of Life uses thirty two colors, not counting black for dead cells.

    Multiple Step Rule Notation

    Individual steps are seperated by plus signs. The following specifies a five step version of Game Of Life with identical steps: 

         3/23 + 3/23 + 3/23 + 3/23 + 3/23

    Repetition is indicated by use of an asterisk preceeded by a count. The following specification is equivalent to the previous specification: 

         5 * 3/23

    Parentheses may be used to group steps together. The following specification is equivalent to the previous two specifications: 

         2 * (3/23 + 3/23) + 3/23

    Ghost Colors

    When multiple step notation is used colors are assigned according to the union of the specification over all steps. Ghost color values will appear in steps lacking a particular specification which occurs in other steps. Consider the following example: 

         37/23 + 38/23
    Colors are assigned to all steps based upon "378/23". Depending upon the step it might appear as if a new birth is to take place in a cell with seven or eight neighbors when no birth actually takes place.

    Here is an example of ghost colors, the "Just For Fun" multiple step rules. Watch closely! Because of ghost colors it will appear as if part of the rule (the "356/0246" part) is functioning incorrectly.

    Game Of Life Links

    Good sites for furthur exploration of Conway's Game Of Life:
  • DMOZ Open Directory Project Conway's Game Of Life category
  • Yahoo's Conway's Game Of Life category
  • David Bell's Homepage
  • Paul Callahan's Game of Life page
  • David Eppstein's Gliders in Life-like Systems
  • Alan Hensel's Conway's Game of Life
  • Dean Hickerson's Game of Life page
  • Jason Summer's Jason's Life Page

    Other Cellular Automata Sites and Software by George Maydwell

    Modern Cellular Automata is a sister site which explores color cellular automata rules (like the ones above) which are not too closely related to Game Of Life. Many rules are on display, including hexagonal rules. Finally, the free Modern Cellular Automata authoring tools are available for downloading from the site.

    Collidoscope is fast (sixty frames per second) hexagonal color cellular automata software for Windows which operates as a screen saver and turns one's computer into a large scale emergence appliance. With a wide variety of rules and a user interface which is trivial, Collidoscope lets anyone surf cellular automata rule space. Collidoscope 1.1 has just been released.

    SARCASim is fast programmable color cellular automata software for Windows, the predecessor to Collidoscope. Its powerful enough that it supports both hexagonal and rectangular geometries as well as arbitrary cell neighborhoods.