sidef-scripts/Math/elementary_cellular_automaton_generalized.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 16 October 2019
# https://github.com/trizen

# Generalization of the elementary cellular automaton, by using `n` color-states and looking at `k` neighbors left-to-right.

# For example, a value of `n = 3` and `k = 2` uses three different color-states and looks at 2 neighbors to the left and 2 neighbors to the right.

# See also:
#   https://en.wikipedia.org/wiki/Cellular_automaton
#   https://en.wikipedia.org/wiki/Elementary_cellular_automaton
#   https://rosettacode.org/wiki/Elementary_cellular_automaton

# YouTube lectures:
#   https://www.youtube.com/watch?v=S3tYzCPuVsA
#   https://www.youtube.com/watch?v=pGGIE5uhPRQ

func automaton(n, k, callback, rule=120, iter=50, cells=[1]) {

    var states = @(^n).variations_with_repetition(2*k + 1)
    var digits = rule.digits(n)
    var lookup = Array()

    for i,s in (states.kv) {
        lookup[s.digits2num(n)] = digits[i]\\0
    }

    var padding = ((iter-cells.len)/2 -> of(0))
    cells = [padding..., cells..., padding...]

    var len = cells.len
    var neighbors_range = @(-k .. k)

    (iter/2).times {
        callback(cells)
        cells[] = lookup[
            cells.range.map { |i|
                neighbors_range.map {|j| cells[(i+j) % len] }.digits2num(n)
            }...
        ]
    }

    return cells
}

var chars = [' ', '*', '.', '#']

say "\n=> 2x1 Automaton"

automaton(2, 1, rule: 90, callback: {|row|
    say row.map { chars[_] }.join
})

say "\n=> 3x1 Automaton"

automaton(3, 1, rule: 843693805713, callback: {|row|
    say row.map { chars[_] }.join
})

say "\n=> 3x2 Automaton"

automaton(3, 2, rule: 590193390821886729275563552433397050190, iter: 80, callback: {|row|
    say row.map { chars[_] }.join
})