Class one cellular automata

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Class one cellular automata, according to the classification system of Stephen Wolfram, are those where the development of all patterns tends towards vacuum.

Class one has many similarities to class two cellular automata. It is in several cases simple to prove that no growth pattern can exist in a Life-like or closely related cellular automaton. Showing the nonexistence of still lifes or oscillators can be, however, more difficult. As such, it can be difficult to distinguish class two CA whose ash has extremely low density from class one.

It is debatable whether agar solutions are sufficient to claim a CA as class two and not class one. As an extreme example, in the Life-like CA B/S8, exactly one pattern exists that does not evolve to vacuum: "antivacuum", the infinite field of live cells.

Given their highly predictable nature, there has been very little interest in detailed investigation of class one automata, and none appear to have established names.

See also