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Rule 90
Rule space information
rule type | elementary cellular automaton rule space | 2-color, range 1 (3-cell neighborhood) number of rules | 256
Rule icon
| 1 | | 0
Rule equivalences
left-right | color | both rule 90 | rule 165 | rule 165 (total: 3)
Boolean form
(p, q, r) ↦ p XOR r
Algebraic form
(p, q, r) ↦ (p + r) mod 2
Neighbor dependency
linear | none | linear
Evolution from simple initial condition
Evolution from random initial conditions
Typical difference patterns
Properties
Rule 90 is an additive rule.
Rule 90 is left-right symmetric.
The generating function for rule 90 is 1/(1 - (x + 1/x) y) (mod 2).
Rule 90 is a class 3 rule from random initial conditions.
Rule 90 is an outer totalistic rule, corresponding to outer totalistic code 12.
Finite-size state transition diagrams
| | | | size 2 | size 3 | size 4 | size 5 | size 6