One dimensional Cellular Automata

DCA(rule; states=2, radius=1)

Construct a discrete cellular-automaton rule and its neighborhood lookup table.

Arguments

• rule: Nonnegative Wolfram rule identifier.

Keyword arguments

• states: Number of possible cell states. Defaults to 2.
• radius: Symmetric radius or (left, right) asymmetric radius. Defaults to 1.

Throws

• ArgumentError: If the rule configuration or a transitioned state is outside its declared discrete domain.

Examples

julia> using CellularAutomata

julia> dca = DCA(30);

julia> rule_lookup_table(dca)
8-element Vector{Int64}:
 0
 1
 1
 1
 1
 0
 0
 0

julia> next_state(dca, [0, 0, 1, 0, 0])
5-element Vector{Int64}:
 0
 1
 1
 1
 0

TCA(code; states=2, radius=1)

Construct a totalistic cellular-automaton rule and its lookup table.

Arguments

• code: Nonnegative totalistic rule identifier.

Keyword arguments

• states: Number of possible cell states. Defaults to 2.
• radius: Symmetric radius or (left, right) asymmetric radius. Defaults to 1.

Throws

• ArgumentError: If the rule configuration or a transitioned state is outside its declared discrete domain.

Examples

julia> using CellularAutomata

julia> tca = TCA(3);

julia> rule_lookup_table(tca)
4-element Vector{Int64}:
 1
 1
 0
 0

julia> next_state(tca, [0, 0, 1, 0, 0])
5-element Vector{Int64}:
 1
 1
 1
 1
 1

CCA(rule; radius=1)

Construct a continuous cellular-automaton rule. Each output is the fractional part of the neighborhood mean plus rule.

Arguments

• rule: Value added to each neighborhood mean.

Keyword arguments

• radius: Symmetric radius or (left, right) asymmetric radius. Defaults to 1.

Examples

julia> using CellularAutomata

julia> cca = CCA(1 // 10);

julia> next_state(cca, [0 // 1, 0 // 1, 3 // 10])
3-element Vector{Rational{Int64}}:
 1//5
 1//5
 1//5

CellularAutomatonRNG(rule=DCA(30); size=127, seed=rand(RandomDevice(), UInt),
    skip=nothing, start=nothing, warmup=4) -> CellularAutomatonRNG

Pseudorandom number generator driven by a one-dimensional cellular automaton, in the style of Wolfram's original Rule 30 generator (Mathematica's "ExtendedCA" method). Only binary rules are supported: mapping a correlated multi-state CA stream to unbiased bits requires assumptions that the generic rule interface cannot guarantee. The seed is mixed across a tape of size cells. The automaton is then advanced for warmup * size throwaway generations before output begins. Each subsequent generation advances the automaton and reads one or more cells as output bits.

By default only the center cell is read, one bit per generation. Passing skip reads every skip-th cell starting from start across the whole tape instead, producing many bits per generation for much higher throughput, the same trick "ExtendedCA" uses (there with Skip=4) to avoid the correlation between adjacent cells that a finite-radius rule would otherwise introduce within a single generation.

Arguments

• rule: Binary one-dimensional discrete cellular-automaton rule driving the tape. Custom rules must implement cell_state_count(rule). Defaults to DCA(30).

Keywords

• size: Number of cells on the tape. Even values are bumped up by 1 to keep a well-defined center cell. Defaults to 127.
• seed: Integer mixed across the initial tape. Defaults to a seed drawn from the OS entropy source (RandomDevice()).
• skip: When nothing (the default), read only the cell at start. Otherwise, read every skip-th cell starting from start across the tape each generation.
• start: Index of the first cell read each generation. Defaults to the center cell when skip is nothing, or to 1 when skip is given.
• warmup: Number of throwaway generations per tape cell after initialization. Defaults to 4.

Throws

• ArgumentError: If rule does not implement cell_state_count, if the rule is not binary, if size is smaller than 3, if skip is smaller than 1, if start is outside 1:size, or if warmup is smaller than 1.

Examples

julia> using CellularAutomata

julia> rng = CellularAutomatonRNG(DCA(30); size = 7, seed = 1);

julia> rand(rng, UInt8)
0xb7

julia> wide_rng = CellularAutomatonRNG(DCA(30); size = 15, seed = 2, skip = 4);

julia> rand(wide_rng, UInt8)
0xd4