Step: 0
Coupled Map Lattice
x_i(t+1) = (1−ε)f(x_i) + ε/2[f(x_{i-1})+f(x_{i+1})]
f(x)=rx(1−x) is the logistic map. Spacetime diagram: each row is one time step, each column is a lattice site.
r≈3.57: onset of chaos. r=4: fully chaotic. Coupling ε smooths spatial structure, creating spatio-temporal patterns.
x_i(t+1) = (1−ε)f(x_i) + ε/2[f(x_{i-1})+f(x_{i+1})]
f(x)=rx(1−x) is the logistic map. Spacetime diagram: each row is one time step, each column is a lattice site.
r≈3.57: onset of chaos. r=4: fully chaotic. Coupling ε smooths spatial structure, creating spatio-temporal patterns.