Coupled Map Lattice: Spatiotemporal Chaos

Locally coupled chaotic maps display traveling waves, frozen chaos, and synchronization transitions.

r = 3.85
ε = 0.100
L = 140
Phase: chaos  |  ⟨x⟩ =  |  σ(x) =  |  Step: 0
CML update: x_i(t+1) = (1−ε) f(x_i(t)) + ε/2 [f(x_{i-1}(t)) + f(x_{i+1}(t))]
where f(x) = r·x·(1−x) is the logistic map.
Space-time plot: each column = lattice site, each row = time step (newest at top).
Color encodes x value: dark (low) → gold (mid) → bright (high). Increasing coupling ε drives the system toward synchronization.