PlayTurn the knobs yourself

The static pages drew chaos once. Here it runs live: every demo steps the same equations in your browser as you drag. Nothing is pre-recorded — you are computing it.

Reads best on a wide screen. Motion respects your reduced-motion setting.

1 · The logistic lab

Drag the growth knob r. The staircase on the left, the beat over time in the middle, and the whole family on the right all update as you move it. Click the family picture to jump the knob straight to any setting — watch one value split to two, to four, then into the fog.

2 · Two starts, a hair apart

Set how close the two starts are, and the growth knob. They track as one line, then part. Widen the gap and they part later; tighten it and chaos still pulls them apart — it only takes longer.

3 · The Lorenz butterfly, live

The weather model, drawing itself. Turn ρ down and it settles to a point or a loop; turn it up past about 24.7 and the butterfly opens. Switch on the twin to release a second start a thousandth away and watch the gap between them grow.

4 · The law of large numbers

Roll the die. One roll is anyone's guess; keep the running average and it is reeled in to 3.5. The shaded funnel is how far off to expect, and it closes as one over the square root of the number of rolls.

5 · The governor

Two tanks take the same run of random shocks. The red one has no feedback and wanders off; the green one subtracts a share of its own error every step and holds near centre. Drag the pull-back, and hit it with a shock to see it recover.