Coupled map lattice

Choose r, coupling ε and a starting row, then Render. The ring uses f(x)=r·x·(1−x) and xᵢ(t+1)=(1−ε)f(xᵢ)+ε/2·[f(xᵢ₋₁)+f(xᵢ₊₁)], with periodic neighbors. All sites update together from the old row. At ε=0 the sites evolve independently; a uniform row stays uniform at every coupling.

Render starts from the chosen row, discards the burn-in and draws 320 consecutive rows. One step and Run apply the same burn-in when starting a new history. One step then advances once; Run continues until Pause or navigation. Time labels are actual iteration numbers; after 320 stored rows the window rolls forward. Colors always represent x between 0 and 1, so maps share the same scale.

Uniform fills every site with the initial value. Impulse puts that value at the central site and zero elsewhere. The random mix uses a deterministic 32-bit LCG seed: each site chooses the high interval [0.25,0.75) with the selected probability, otherwise [0,0.15). The share is a probability, not a guaranteed exact fraction of sites. Model edits discard the old history; palette changes only recolor it. Playback interval changes pause without altering the existing values.

This is an illustrative discrete model, not a measurement of a material or an automatic chaos/synchronization classification. Float64 trajectories in chaotic regimes are sensitive to rounding. Reference: Coupled logistic maps and non-linear differential equations. The chosen initialization and rolling display are product conventions. Everything computes in the browser.

Only input values are remembered in this browser. Calculated results and experiment histories are not saved.