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

Vary each control and watch the rail readouts respond.
Compare the diagnostic plot against the live scene.