How many steps do two orbits that start 0.001 apart stay together? At r = 3.9 teal and orange share a row (white) for the first few columns, then split into two unrelated zigzags after about 8.
Try this Set r to 3.2 and press Reset (r also takes effect live, but Reset redraws from the left edge). Both orbits settle onto the same two-value cycle, about 0.51 and 0.80: every column turns white and divergence drops to 0.
About this model Where it ends up
The logistic map x → r·x·(1 − x) is a one-line model of a population with limited resources. Robert May's 1976 review in Nature showed that as r rises the map goes from a fixed point through period doubling to chaos beyond r ≈ 3.57, where orbits that start close together separate exponentially fast. This model plots two such orbits side by side.
The board is a strip chart with 61 rows for x from 0 to 1. Setup starts orbit A at x0 and orbit B at x0 + epsilon and paints the first column. Each tick applies the map to both and paints the next column: A teal, B orange, white where both round to the same row (rows are 1/60 apart). The run stops after 88 ticks, at the right edge. r is read every tick; x0 and epsilon apply at Reset.
The model shows sensitive dependence at one r at a time; it does not draw the bifurcation diagram. It has no randomness, so the same settings always give the same picture.
