Mandelbrot Rainbow Explorer

The Mandelbrot set is the set of complex numbers c for which the iteration z_n+1 = z_n² + c, started from z₀ = 0, stays bounded. Click anywhere on the canvas to recenter on that complex coordinate, or pick a preset target and let the auto-zoom drive into it. The iteration cap rises with zoom depth so deep boundary structure stays resolved. The double-precision floor sits near width 1e-13, after which pixel coordinates collide.

Figure 1. Mandelbrot set rendered by per-pixel iteration of z_n+1 = z_n² + c from z₀ = 0, with continuous escape-time hue mapping (1024-step palette, log(1 + mu) phase). Cardioid and period-2 bulb membership tested in closed form to skip the iteration loop. maxIter scales with zoom depth: 256 at the full set, ~ 2200 at zoom 1e9x.

Jump to preset target

WHAT TO TRY

Click anywhere to recenter and let it auto-zoom: the boundary of the set is infinitely detailed, and every dive reveals miniature copies of the whole Mandelbrot shape. The colour bands count escape time.
Jump to a named landmark (Seahorse Valley, a satellite mini-set, the elephant valley): each is a different self-similar structure on the fractal boundary.
Raise maxIter as you zoom deeper: the black interior sharpens, since points that look bounded at low iteration counts eventually escape. Detail costs iterations.