FRACTAL EXPLORER

Drag to pan, scroll or pinch to zoom, and the URL follows you — every view is a link. Colouring is the continuous escape estimate, not the raw iteration count, which is why the bands have no stair-steps in them.

Each pixel is one complex number c, and the only question asked of it is whether iterating z → z² + c from zero stays bounded. It either escapes past radius 2 — after which it is gone for good — or it never does. Black is “never did, within the iteration limit”, so raising that limit shrinks the black and reveals thinner filaments; the limit is the only thing between you and an exact answer.

Everything is computed in double, which runs out at roughly 10¹⁵× magnification — past that, neighbouring pixels round to the same complex number and the image goes blocky. Going deeper needs arbitrary-precision arithmetic with perturbation theory, which is a different program. The readout says when you are close.

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