🌀 Mandelbrot Set Explorer

The Mandelbrot set is the set of complex numbers c for which the iteration z → z² + c (starting at z = 0) stays bounded forever. Points inside the set are colored black; points outside are colored by how quickly they escape to infinity. Named after Benoit Mandelbrot, who studied it in 1980, it is the most famous example of a fractal — an object whose intricate, self-similar structure repeats at every scale.

For each pixel the tool maps its position to a complex number c, then iterates z² + c until the magnitude exceeds 2 (guaranteed escape) or the iteration cap is reached. The escape count drives the color. This explorer uses smooth (continuous) coloring — a fractional escape value computed from the final magnitude — so bands blend seamlessly instead of forming hard rings. Rendering runs in row-bands via requestAnimationFrame so the page stays responsive even at 1000 iterations.

As you zoom deeper, raise the iteration count: shallow views look fine at 100–200 iterations, but deep zooms need 500–1000 to resolve fine filaments. The most spectacular structures — miniature Mandelbrots, spirals and "seahorse" valleys — live along the boundary between the black interior and the colored exterior. When you find a view you like, click Save PNG to export it at full canvas resolution.