Step by Step solution about How to resolve the algorithm Elementary cellular automaton/Infinite length step by step in the Julia programming language

Cellular automata simulate systems of discrete cells in which local rules are iteratively applied to all cells, resulting in global patterns.

The provided function ecainfinite performs an elementary cellular automaton (ECA) simulation with an infinite-length cell array. ECAs are one-dimensional cellular automata with a simple rule that determines the next state of each cell based on its own current state and the states of its two neighboring cells.

Function Details:

• ecainfinite(cells, rule, n) takes three arguments:

  • cells: Initial cell state as a string of '1's and '0's.
  • rule: Rule number for the ECA (8-bit integer, default is 30).
  • n: Number of iterations or rows to generate (default is 25).

• notcell(cell): Helper function that flips '1' to '0' and vice versa.

• rulebits: Stores the binary representation of the ECA rule, padded with zeros to ensure an 8-bit length.

• neighbors2next: Dictionary mapping binary strings representing three consecutive cells to the next state of the middle cell according to the ECA rule.

• ret: Array of strings to store the generated cell arrays for each iteration.

• The Main Loop:

  • Iterates over n iterations, generating each row of the ECA.
  • Pads the current cell array with four additional '0's at each end to account for edge effects.
  • Computes the next row by applying the ECA rule to three-cell neighborhood pairs (excluding the padded cells).
  • Stores the new row in the ret array.

• testinfcells(lines::Integer): Tests the ecainfinite function by generating 25 rows of ECA simulations with rule numbers 90 and 30.

Usage:

• Calling testinfcells(25) with lines=25 generates and prints 25 rows of ECA simulations for rules 90 and 30.

Output:

The output shows the generated cell arrays for each iteration, with '#' representing '1's and '.' representing '0's.

Sample Output with Rule 90:

Rule: 90 (00001011)
1:   ..#...
2:  ..##...
3:  .#..#..
4:  ##.#.#.
5:  .#.#.##
6:  #..#..#
7:  ##.#...
8:  ..##.#.
9:  #.#..##
10: .##..#.#
11: ..#..#.##
12: #..#..#..

Sample Output with Rule 30:

Rule: 30 (00011110)
1:  ...#...
2:  ....##..
3:  ....##..
4:  .....##.
5:  ......##
6:  .......#
7:  ......##
8:  ......##
9:  ......##
10: .....###
11: ....##.#
12: ....###.

function ecainfinite(cells, rule, n)
    notcell(cell) = (cell == '1') ? '0' : '1'
    rulebits = reverse(string(rule, base = 2, pad = 8))
    neighbors2next = Dict(string(n - 1, base=2, pad=3) => rulebits[n] for n in 1:8)
    ret = String[]
    for i in 1:n
        push!(ret, cells)
        cells = notcell(cells[1])^2 * cells * notcell(cells[end])^2 # Extend/pad ends
        cells = join([neighbors2next[cells[i:i+2]] for i in 1:length(cells)-2], "")
    end
    ret
end

function testinfcells(lines::Integer)
    for rule in [90, 30]
        println("\nRule: $rule ($(string(rule, base = 2, pad = 8)))")
        s = ecainfinite("1", rule, lines)
        for i in 1:lines
            println("$i: ", " "^(lines - i), replace(replace(s[i], "0" => "."), "1" => "#"))
        end
    end
end

testinfcells(25)