Deficient rule

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Deficient rules are a generalisation of regular 2-state isotropic non-totalistic cellular automaton. In deficient rules, the same birth / survival condition may not be used more than once in a row. They were conceived by 83bismuth38.[1]


Deficient rules are described by rulestrings of the form Bb/Ss/Dd; where b, s and d are isotropic non-totalistic transitions.

We write n ∈ B, n ∈ S, n ∈ D if n is one of the transitions in b, s, d and m is the state that maps to the isotropic transition n; patterns then evolve according to the following rules:

  1. A dead cell (state == 0)
    1. Is born into state 1 if n ∈ B and not n ∈ D
    2. If not, it is born into state m if n ∈ B and n ∈ D and state m is not in the cell's neighbourhood
    3. If not, it stays dead
  2. A deficient cell (state > 1)
    1. Becomes a living cell if n ∈ S
    2. If not, it becomes a dead cell
  3. A living cell (state == 1)
    1. Stays alive if n ∈ S
    2. If not, it becomes a dead cell

Software support

Deficient rules are not natively supported by Golly or LifeViewer (support is planned for the latter),[2] but can be run with a suitable ruletable on either. Catagolue and apgsearch also support Deficient rules but with the selective deficiency of certain birth transitions.[3]


  1. 83bismuth38 (April 18, 2018). Re: Deficient Rules (discussion thread) at the forums
  2. Chris Rowett (January 26, 2019). Re: Pattern viewer for forum threads (discussion thread) at the forums
  3. Adam P. Goucher (January 15, 2019). "Native support for Extended Generations and Deficient rules courtesy of M. I. Wright". GitLab.