ca_evolution.py

import numpy as np

def cellular_automaton(rule_number, size, steps,
                       init_cond='random', impulse_pos='center'):
    """Generate the state of an elementary cellular automaton after a pre-determined
    number of steps starting from some random state.

    Args:
        rule_number (int): the number of the update rule to use
        size (int): number of cells in the row
        steps (int): number of steps to evolve the automaton
        init_cond (str): either `random` or `impulse`. If `random` every cell
        in the row is activated with prob. 0.5. If `impulse` only one cell
        is activated.
        impulse_pos (str): if `init_cond` is `impulse`, activate the
        left-most, central or right-most cell.

    Returns:
        np.array: final state of the automaton
    """
    assert 0 <= rule_number <= 255
    assert init_cond in ['random', 'impulse']
    assert impulse_pos in ['left', 'center', 'right']
    
    rule_binary_str = np.binary_repr(rule_number, width=8)
    rule_binary = np.array([int(ch) for ch in rule_binary_str], dtype=np.int8)
    x = np.zeros((steps, size), dtype=np.int8)
    
    if init_cond == 'random':  # random init of the first step
        x[0, :] = np.array(np.random.rand(size) < 0.5, dtype=np.int8)

    if init_cond == 'impulse':  # starting with an initial impulse
        if impulse_pos == 'left':
            x[0, 0] = 1
        elif impulse_pos == 'right':
            x[0, size - 1] = 1
        else:
            x[0, size // 2] = 1
    
    for i in range(steps - 1):
        x[i + 1, :] = step(x[i, :], rule_binary)
    
    return x