Spatiotemporal chaos and synchronization
A Coupled Map Lattice (CML) is a spatially-extended dynamical system: xᵢ(t+1) = (1−ε)f(xᵢ(t)) + (ε/2)[f(xᵢ₋₁(t)) + f(xᵢ₊₁(t))] where f(x) = rx(1−x) is the logistic map. Space-time patterns show traveling waves, synchronized chaos, defect turbulence, and phase separation depending on coupling strength ε and nonlinearity r. Color encodes the local state value over time.