pyCA.eca module

Elementary cellular automata.

An elementary cellular automaton (ECA) is the simplest interesting dynamical system there is: a periodic row of cells, each 0 or 1, each updating from its own value and its two neighbors’ values according to one of the 256 possible rules. Stephen Wolfram’s numbering names each rule by the byte whose bit n gives the output for the neighborhood whose (left, center, right) values read, as a binary number, n.

The ECA class mirrors the original MATLAB implementation: rule and state are validated properties that can be reassigned at any time, evolve advances one step, and play opens a live spacetime display.

class pyCA.eca.ECA(rule, state=None, N=64, memory=None, rng=None)

Bases: object

A 1-dimensional elementary cellular automaton on a periodic lattice.

Parameters:

• rule (int) – Wolfram rule number, 0-255.

• state (array_like of 0s and 1s, optional) – Initial state. If omitted, a random state of length N is drawn.

• N (int, optional) – Lattice size used when state is omitted (default 64).

• memory (int, optional) – Number of past states retained for spacetime and play. Defaults to max(min(3*N, 5000), 300), matching the MATLAB class.

• rng (numpy.random.Generator, optional) – Random source; defaults to numpy.random.default_rng().

rule

The rule number. Reassigning it rebuilds the lookup table.

Type:

int

state

The current state. Reassigning it appends to the history.

Type:

ndarray

N

Lattice size.

Type:

int

Examples

>>> from pyCA import ECA
>>> ca = ECA(110, N=128)
>>> ca.run(100)
>>> ca.spacetime().shape
(101, 128)

evolve()

Advance the automaton one time step.

play(interval=30)

Open a live spacetime display; close the window to stop.

Parameters:

interval (int, optional) – Milliseconds between frames (default 30).

run(steps)

Advance the automaton steps time steps.

spacetime()

The remembered history as a (time, space) array of 0s and 1s.

Row 0 is the oldest remembered state; the last row is the current state. At most memory rows are kept.