Bedhead attractor: the mint map cloud — Classical Chaos

The Bedhead attractor starts at a seed, applies a short formula, and lands on the next (x, y). Do that again and again and the picture is just the pile. No continuous trail of rates: a discrete 2D map. Classical Chaos paints the body mint-green and the moving tip yellow.

Defaults sit near seed (0.1, 0) with a ≈ 0.65343 and b ≈ 0.7345345. The cloud below grows as more iterates land.

The update rule

Each new point comes only from the last one. No dt, no integrating rates along a curve. The step Classical Chaos runs:

const nextX = Math.sin((x * y) / b) * y + Math.cos(a * x - y)
const nextY = x + Math.sin(y) / b
x = nextX
y = nextY

b sits in a denominator, so the step must not hit zero. On the full stage the b knob floors above zero; some (a, b) pairs still send samples flying, and the stage clamps extreme values so the view stays usable.

Twisting a and b

Small moves on a and b can reshape the whole silhouette. On the full Bedhead stage those knobs sit next to example presets: the default pair, then jumps like (−0.64, 0.76) and (0.06, 0.98). Change either constant and the cloud redraws from the seed.