Module forma.automata

Pattern manipulation with Cellular Automata.

Cellular Automata are defined here by a ruleset (a table of individual CA rules). Each rule consists of two parts. Firstly a neighbourhood that the rule acts on. Secondly a rule signature specifying the conditions under which cells are Born (B) or Survive (S). These rule signatures are initialised with a string in the "Golly" format. i.e a rule which activates cells with one neighbour and deactivates cells with two would have the rule string "B1/S2". The neighbourhood is specified by an instance of the forma.neighbourhood class as usual.

Once a ruleset is specified, there are two provided implementations of a CA. Firstly the standard synchronous CA is implemented in automata.iterate whereby all cells are updated simultaneously. Secondly an asynchronous update is provided in automata.async_iterate in which each iteration updates only one cell at random.

When a ruleset consists of only one rule, the CA is unambiguous and is applied in the conventional manner. When multiple rules are provided, rule conflicts are resolved in favour of cell deactivation. For example, if there are two rules in the set, cell activation requires that the candidate cell passes the 'birth' criterion of both rules. Cell deactivation requires only that one 'survive' criterion fails.

All CA updates here are only possible on a finite domain of cells. That domain must be specified as a pattern in the iteration call.

Both the synchronous and asynchronous iterations return the result of one CA iteration and a bool specifying whether or not the iteration has converged to a stable pattern.

Relevant examples

Ruleset Generation

rule (neighbourhood, rule_string) Define a cellular automata rule.

CA Iteration

iterate (prevp, domain, ruleset) Synchronous cellular automata iteration.
async_iterate (prevp, domain, ruleset, rng) Asynchronous cellular automata iteration.


Ruleset Generation

rule (neighbourhood, rule_string)
Define a cellular automata rule. CA rules in forma are defined by a neighbourhood in the usual CA sense and a string signature in the 'Golly' format (BXX/SXX). This function initialises a rule, and performs a few consistency checks.

Parameters:

  • neighbourhood specifying the neighbourhood the rule is to be applied in.
  • rule_string string specifying the ruleset (i.e B23/S1).

Returns:

    A verified rule for use with the CA methods.

Usage:

    -- Initialise a rule corresponding to Conway's Game of Life
    local gol_rule = automata.rule(neighbourhood.moore(), "B3/S23")

CA Iteration

iterate (prevp, domain, ruleset)
Synchronous cellular automata iteration. Performs one standard synchronous CA update on pattern prevp in the specified domain.

Parameters:

  • prevp the previous iteration of the pattern
  • domain the cells in which the CA operates
  • ruleset a table of forma.rules defining the CA

Returns:

  1. The result of the CA iteration [pattern].
  2. Convergence flag [bool: true if converged, false otherwise].

Usage:

    -- Domain and initial state (500 seed points) for the CA
    local domain = primitives.square(100)
    local ca_pat = subpattern.random(domain, 500)
    -- Repeat iteration until convergence is reached
    local converged = false
    repeat
    	ca_pat, converged = automata.iterate(ca_pat, domain, {gol_rule})
    until converged == true
async_iterate (prevp, domain, ruleset, rng)
Asynchronous cellular automata iteration. Performs a CA update on one cell (chosen randomly) in the specified domain. This corresponds to a 'random independent scheme' update.

Parameters:

  • prevp the previous iteration of the pattern
  • domain the cells in which the CA operates
  • ruleset a table of forma.rules defining the CA
  • rng a (optional) random number generator (syntax as per math.random).

Returns:

  1. The result of the CA iteration [pattern].
  2. Convergence flag [bool: true if converged, false otherwise].

Usage:

    -- Domain and initial state (10 seed points) for the CA
    local domain = primitives.square(10)
    local ca_pat = subpattern.random(domain, 10)
    local rng    = math.random
    -- Repeat iteration until convergence is reached
    local converged = false
    repeat
    	ca_pat, converged = automata.async_iterate(ca_pat, domain, {gol_rule}, rng)
    until converged == true
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