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