Theme

Small rules, large behaviour — page 3

Rules short enough to write on one line, producing behaviour nobody can summarise — and the finding that the size of a rule predicts nothing about the difficulty of the questions it raises.

Two chaotic maps, coupled weakly and strongly. The gap between two coupled copies of the logistic map at full chaos: at ε = 0.15 it stays large; at ε = 0.3 it falls to nothing.

Dynamics

Two chaotic orbits made to agree

Chaos means two copies of a system started a hair apart soon have nothing in common. Couple them — let each take a fraction ε of its next step from the other — and above a definite strength they agree to every digit for ever, while each stays exactly as chaotic as before. The strength needed is read off the same number that measured the chaos: the Lyapunov exponent.

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