A Coupled Map Lattice (CML), introduced by Kunihiko Kaneko (1984), is a minimal model for spatiotemporal chaos. Each lattice site i has a state xᵢ updated by:
where f is a chaotic local map (logistic: f(x)=rx(1−x)) and ε is the coupling strength. CMLs exhibit a rich phase diagram: coherent (synchronized, ε large), frozen random (spatial disorder, ε small), pattern selection, chaotic travelling waves, and spatiotemporal intermittency. The space-time diagram here (each row = one time step, color = x value) reveals the turbulent structure. CMLs are widely used to model coupled oscillators, reaction-diffusion systems, and neural networks, offering an analytically tractable route into high-dimensional chaos.