🌌 Julia Set Generator

For a fixed complex constant c, the Julia set is the set of starting points z for which the iteration z → z² + c stays bounded forever. Every value of c produces a completely different fractal. When c lies inside the Mandelbrot set the Julia set is a single connected shape; when c lies outside, it shatters into a scattered dust of infinitely many disconnected points.

The Mandelbrot set is effectively the atlas of all Julia sets: each point on it corresponds to one Julia set, and whether that Julia set is connected or dust is decided by which side of the Mandelbrot boundary c falls on. Moving the real and imaginary sliders here is exactly like walking a pointer around that map — nudge c across the boundary and you watch a solid fractal dissolve into dust and back.

Julia sets are extremely sensitive: a tiny change in c can transform the shape completely, so drag the sliders slowly and explore near the edges. Raise the iteration count to sharpen fine filaments and boundary detail, and lower it for a faster, softer render. Try the presets — Spiral, Dendrite, Galaxy and Lightning each sit at a famous value of c. When you find one you love, click Save PNG to export it at full resolution.