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The rulespace is the totality of rules described by some form of notation, e.g. a certain kind of rulestrings.

The term "rulespace" may be qualified to include only rules with certain attributes, e.g. certain birth or survival conditions; the exact rules included may vary in different contexts. For example, "B3 rulespace" may be taken to include outer-totalistic Life-like cellular automata such as Conway's Game of Life (B3/S23) and Day & Night (B3678/S34678), while excluding such rules as Seeds (B2/S).

"D" ("death") conditions are sometimes used to indicate that certain survival conditions should not be included; thus, for example, the "B0/D8 rulespace" would include all rules where dead cells with no live neighbors get born in one generation, but live cells surrounded entirely by live neighbors then die again in the next generation. "A" conditions are used in the same manner to indicate that certain birth conditions should not be included; for instance, "A2 Generations rules" would include all Generations rules without B2, and "S23·D1456/B34·A5/3 rules"[1] would include all 3-state Generations rules with B34/S23 and without any of B5/S1456.

Macbi partial notation

An alternative notation for describing isotropic non-totalistic rulespaces was devised by Oscar Cunningham (Macbi) to be used with LLS. All partial rules begin with the prefix p to distinguish them from exact rules with the same rulestring. In this notation, a numerical transition without any letters specified is assumed to have all of its letter transitions optional. Letters that are listed are either forbidden (if they come before a - sign) or required otherwise.[2] For example, the string pB3aei67e-c8/S2aceikn3aei indicates that:

  • the transitions B3aei, B7e, all S2 transitions, and S3aei are required;
  • all other B3 and S3 transitions are optional, as well as all B6 and B8 transitions;
  • all other transitions are forbidden.


  1. Re: 238/346/3 (discussion thread) at the forums
  2. Oscar Cunningham. Re: Logic Life Search (discussion thread) at the forums