Mandelbrot and Julia sets

Both images are computed from the quadratic iteration z ↦ z² + c. The Mandelbrot set varies c and starts at z = 0; the Julia set fixes c and starts at each pixel z = x + iy. Escape radius is |z| > 2, with smooth coloring.

Mandelbrot set

z_n+1 = z_n² + c, z₀ = 0

Iteration depth: 250

Drag to pan, scroll to zoom, or use zoom buttons. A click without dragging sets the Julia parameter c.

Julia set

z_n+1 = z_n² + c, z₀ = x + iy

c real:

c imaginary:

Drag to pan, scroll to zoom, or use zoom buttons. Sliders control the fixed c.

``` Key choices: - **Resolution:** 640 × 640 per fractal, with a 128 × 128 preview shown immediately while the full image renders progressively. - **Iteration depth:** default 250, adjustable from 64 to 1024. - **Escape test:** `|z|² > 4`, i.e. escape radius 2. - **Coloring:** smooth continuous iteration count mapped through a 2048-entry cosine palette. - **Mandelbrot view:** centered at `-0.75 + 0i`, half-span `1.75`, showing the whole recognizable set. - **Julia view:** centered at `0 + 0i`, half-span `1.6`, with initial `c = -0.743643 + 0.131825i`, a recognizable rabbit Julia set. - **Interactivity:** drag to pan, scroll to zoom, zoom buttons, Julia `c` sliders, click Mandelbrot to choose Julia `c`, random connected `c`, reset views.