Fractal Dream: four sines, one folded cloud — Classical Chaos

Fractal Dream is a flat point cloud that folds as you watch it grow. Discrete map, not a continuous flow: take (x, y), run a short sine rule, land on the next point, pile those samples until a silhouette shows up.

Defaults sit at seed (−2, −2) with a = 1.1, b ≈ 2.764, c = 1.07, d = 1.561. The cloud below thickens as more iterates land.

The update rule

Each new point comes only from the last one. No dt. The step Classical Chaos runs:

const nextX = Math.sin(b * y) + c * Math.sin(b * x)
const nextY = Math.sin(a * x) + d * Math.sin(a * y)
x = nextX
y = nextY

Four real knobs: a, b, c, d. Crossed arguments do the work: b mixes into both sine terms that build x, a into both that build y. c and d scale the second sine on each line. About on the stage lists the limits as [0, 3] for all four.

Clifford-style maps sit nearby as cousins. Those usually mix sine and cosine. Fractal Dream here is all sine, which for some params reads a bit more symmetric. No single famous discoverer to pin on this spelling; the canvas just runs the map above.

Full canvas

On the full Fractal Dream stage twist a, b, c, d inside [0, 3] and watch the same seed rebuild into a different fold.