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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

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