Cellular Automata From First Principles 21: Sensitivity to Initial Conditions

Mon, 10 Aug 2026 18:54:00 +0100

Change one cell.

Then run the same rule twice.

If the two futures remain almost identical, the rule is insensitive to that perturbation.

If the difference spreads, the rule amplifies local uncertainty.

That is one of the cleanest experiments we can perform on a cellular automaton.

Create two nearby initial states

import numpy as np

width = 201
base = np.zeros(width, dtype=np.uint8)
base[width // 2] = 1

perturbed = base.copy()
perturbed[width // 2 + 1] ^= 1

The two states differ by exactly one bit.