Coupled Map Lattice — Spatiotemporal Chaos

1D lattice of logistic maps — diffusive coupling creates spatiotemporal chaos, patterns, and synchrony

Map & Coupling

Logistic r3.8

Coupling ε0.3

Lattice size L100

Initial Condition

Colormap

Speed (steps/frame)3

Step0

Mean x—

Std dev—

Regimechaos

CML (Kaneko 1984): xᵢ(t+1) = (1−ε)f(xᵢ(t)) + ε/2[f(xᵢ₋₁(t)) + f(xᵢ₊₁(t))]. Space-time plot shows 350 timesteps (x-axis: site, y-axis: time, color: value). Patterns include: spatiotemporal chaos (high r), traveling waves, frozen random patterns, pattern selection.