mandelbro — Infinite Fractal Zoom in Your Browser

Re: -0.50000000
Im: 0.0000e+0
Zoom: 1.0x
100%

The best Mandelbrot set explorer on the web

Mandelbro is a free, open-source Mandelbrot set rendererthat runs entirely in your browser — no downloads, no sign-up, no server round-trip. Pan with your mouse or finger, scroll to zoom, and the fractal regenerates in real time at any depth. When you cross the precision wall that limits ordinary fractal viewers at about 1014× magnification, Mandelbro automatically switches to an arbitrary-precision perturbation pipeline so you can keep zooming past 1050×.

What is the Mandelbrot set?

The Mandelbrot set is the set of complex numbersc for which the iteration zn+1 = zn2 + c(starting from z0 = 0) does not escape to infinity. Discovered by Benoît Mandelbrot in 1980, its boundary is a fractal curve of Hausdorff dimension 2 — infinitely complex, infinitely self-similar, and one of the most recognizable images in modern mathematics. Zoom in anywhere on the boundary and you will eventually find spirals, dendrites, and miniature copies of the entire set called minibrots.

How Mandelbro renders deep zoom

Naïve Mandelbrot renderers compute every pixel independently using IEEE 754 double-precision floating point, which runs out of digits at about 16 decimals. Below that — roughly 1013viewport height in the complex plane — adjacent pixels round to identical values and the image stops resolving. Mandelbro avoids this by computing one high-precision reference orbit at the view center using arbitrary-precision arithmetic, then deriving every other pixel as a fast double-precision delta from that orbit. This technique, calledperturbation theory, is combined with series approximation so early iterations can be skipped entirely. The result: smooth real-timedeep zoom in a browser tab.

Famous locations to start exploring

The Mandelbrot set has thousands of named regions, but a handful of classic deep-zoom destinations show off its diversity:

Why use Mandelbro instead of another Mandelbrot viewer?

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