Deficient rule

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.

Description

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), 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.