Chaos Lab

Tool · Playground

Coupled-map lattice builder

Kaneko coupled-map lattices: a discrete-space, discrete-time analogue of a PDE built from many copies of a chaotic 1D map, coupled to their neighbours. Configure the topology, the local map, and the coupling, then watch space-time patterns emerge.

Topology

Local map

t = 0

Space-time diagram. x-axis = lattice site, y-axis = time (bottom = newest).

Synchrony order over time

≈1 ⇒ all sites locked to the same value (full synchrony). ≈0 ⇒ spatially incoherent. Crank up ε to see global-mean coupling force synchrony.

Phenomenology to look for

  • Frozen random pattern (small ε, r ≈ 3.85): each site settles to one of multiple coexisting attractors.
  • Pattern selection / domains (intermediate ε): spatial domains of different attractors with travelling fronts.
  • Spatial intermittency: laminar regions punctuated by chaotic bursts spreading through the lattice.
  • Synchronisation (large ε or global mean coupling): all sites lock to a single chaotic trajectory. Synchrony order goes to 1.

Compare with the spatial flow Lorenz-96 and the cellular automata tool.

FAQ

Frequently asked questions