Logistic Map

The logistic map x' = r·x·(1−x) is the canonical one-line route to chaos. Robert May's 1976 survey showed that this single quadratic recurrence runs through fixed points, period doublings, and — past r ≈ 3.57 — fully chaotic orbits where nearby starting values separate exponentially fast.

This model treats the board as a strip chart. Setup seeds two trajectories whose initial conditions differ by the epsilon slider, then each tick iterates both maps and paints the next column: trajectory A in teal, trajectory B in orange, and a bright mark where the two land on the same row. At low r the traces stay locked together; at r near 4 they visibly tear apart after a few dozen generations, and the divergence monitor tracks the gap.