What a Mandelbrot zoom shows
Take a point c on a plane, start at zero and repeat z → z² + c. If the numbers stay small forever, c belongs to the Mandelbrot set; if they run off, it does not (Wikipedia, Mandelbrot set). Colour each outside point by how fast it escapes and the familiar black shape appears, ringed with bands.
The boundary is where the zoom happens. It never smooths out: magnify any piece of it and there are spirals, filaments and small copies of the whole set. Around some points, called Misiurewicz points, the picture repeats itself exactly as you go in, each ring a scaled copy of the last (Wikipedia, Misiurewicz point). Most Mandelbrot zoom videos are a camera falling toward one such point for minutes or hours.
Why deep zooms take so long to render
Every step deeper needs more digits. A graphics card computes in 32-bit floats, good for about seven digits of precision (Wikipedia, single-precision format), so a plain shader runs out of room after some tens of thousands of times of magnification and the picture breaks into blocks. The famous deep zooms reach magnifications written with thousands of digits.
Deep-zoom renderers get there with perturbation: they compute one reference point in very high precision and every other pixel as a small offset from it. Kalles Fraktaler’s page describes exactly that, with series approximation on top. That is the right tool for a record dive. A music visualizer has to draw every frame in a sixtieth of a second while the song plays, so it cannot carry that precision to any depth.
How the Groovalizer zoom works
Mandelbrot Zoom borrows the perturbation idea and pairs it with the self-similar trick. It sits at a Misiurewicz point near c = −1.5437, about 100,000 times closer than the whole set, where the boundary repeats every 2.8 times of magnification. The shader zooms through one repeat and starts the next, and since each repeat matches the last, the motion reads as an endless fall. It runs in real time in a browser tab. The depth is fixed: it never reaches the places a dedicated renderer visits.
The bands are painted with a picture. By default that is “Light and shadow in the Carina Nebula”, an image credited to NASA / ESA, The Hubble Heritage Team (AURA / STScI), and you can swap in a photo of your own. The Fractalize page covers that part.
The music sets the pace. The zoom speeds up as the track gets louder and busier and eases off in quiet passages. Adjust lets you choose what moves it (the mix, the bass, the mids or the highs), add a glow that swells on the beat, change how fast colour streams through the bands, and turn one slider to zoom in, zoom out or hold still.
Other fractal zooms in the same list
Mandelbrot Zoom is one of 20 zoom looks. The closest relatives are Julia Zoom, the Mandelbrot set’s companion family; Mandelbox Zoom, a box-folding fractal; and Kaliset Zoom. The rest dive through Apollonian circle packings, Sierpinski and Koch shapes, Penrose tilings, Droste spirals and more, each with a picture of its own.
They sit among 2,100+ looks in all, including two classic MilkDrop presets by Ryan Geiss with Mandelbrot in their names. The fractal music visualizer page compares Groovalizer with other fractal visualizers.
Groovalizer next to dedicated fractal explorers
| Tool | Runs | Depth | Moves with music |
|---|
| Groovalizer Mandelbrot Zoom | Browser | About 100,000 times, looped | Yes: speed, glow and colour follow the track |
| Kalles Fraktaler | Windows (also works in Wine on Linux) | Very deep: perturbation with a high-precision reference | No audio input advertised |
| XaoS | Windows, Mac or Linux, plus a web version | Continuous real-time zooming | No audio input advertised |
Kalles Fraktaler read from mathr.co.uk/kf and XaoS from xaos-project.github.io in October 2026. Neither page advertises an audio input. Projects change; check the page before you rely on a row.
If you want to steer through the set yourself, pick your own coordinates, or render a zoom past any depth a browser shader can hold, use one of those. Kalles Fraktaler’s page also links tutorials on turning its output into zoom videos. For a zoom that keeps time with a track and comes out as a music video, use Groovalizer.
Making a Mandelbrot zoom video
Open Mandelbrot Zoom in the Studio, add a song or use the microphone, and set the zoom and glow in Adjust. Watching it, fullscreen or on a projector, is free and needs no account.
A free account exports the video at 720p with a small watermark. A clean video is $4.99 on its own, or Pro at $14.99 a month or $144 a year. Choose 16:9 for YouTube or 9:16 for TikTok, Reels and Shorts. The render runs on your own computer, so your audio never leaves it, and a long track takes as long as your hardware needs.