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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

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

Why Club Z!?

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We're Awesome!

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