One dimensional Cellular Automata

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

Creates a DCA object given a specific rule. It automatically computes the ruleset for the provided rule, number of states, and radius.

Arguments

• rule: The rule identifier used for the cellular automaton's evolution.
• states (optional): The number of possible states for each cell. Defaults to 2.
• radius (optional): The neighborhood radius around each cell considered during the evolution. Defaults to 1.

Usage

dca = DCA(30; states=2, radius=1)  # Creates a DCA with rule 30, 2 states, and radius 1.

Once instantiated, the DCA object can evolve a given starting array of cell states through its callable interface:

dca = DCA(110; states=2, radius=1)  # Initialize with rule 110, 2 states, and a radius of 1
starting_array = [0, 1, 0, 1, 1, 0]  # Initial state
next_generation = dca(starting_array)  # Evolve to the next generation

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

Constructs a Totalistic Cellular Automaton (TCA) with a specified code, number of states, and neighborhood radius. It automatically computes the codeset for the provided code and configuration, which is used for the automaton's evolution.

Arguments

• code: An integer or string representing the rule code for the automaton's evolution.
• states (optional): The number of possible states for each cell. Defaults to 2.
• radius (optional): The neighborhood radius around each cell considered during the evolution. Defaults to 1.

Usage

tca = TCA(30; states=2, radius=1)  # Creates a TCA with rule code 30, 2 states, and radius 1.

After instantiation, the TCA object can be used to evolve a given starting array of cell states:

# Initialize TCA with a specific code, default states, and radius
tca = TCA(102; states=3, radius=1)

# Example starting state: a 1D array of cells
starting_array = [0, 2, 1, 0, 1, 2]

# Compute the next generation
next_generation = tca(starting_array)

CCA(rule; radius=1)

Create a Continuous Cellular Automaton (CCA) object.

Arguments

• rule: A numeric code defining the evolution rule for the cellular automaton.
• radius (optional): The radius of the neighborhood around each cell considered for its update at each step. Defaults to 1.

Returns

CCA: A CCA object initialized with the given rule and radius.

Examples

cca = CCA(0.5)

Once created, the CCA object can be used to evolve a given starting array of cell states:

cca = CCA(0.45; radius=1)  # Initialize with rule 0.45 and default radius
starting_array = [0, 1, 0, 1, 0.5, 1]  # Initial state
next_generation = cca(starting_array)  # Evolve to next generation

The evolution is determined by the rule applied to the sum of the neighborhood states, normalized by their count, for each cell in the array.