Mapping a polar grid onto the Mandelbrot Set on iteration at a time. @MathsTown

Mapping a polar grid onto the Mandelbrot Set on iteration at a time. @MathsTown

Uploaded May 2020 | Updated September 2026, 2 weeks ago

Something a little random and a little different today. I've been experimenting with mapping images into the Mandelbrot and Julia Sets. In this case I've mapped an image of a polar grid (the first image) into the Mandelbrot Set (final image). You can watch this video to see how it evolves step-by-step. (This video has no sound).

You'll notice that the origin (centre of the original graph) returns to each bulb in a periodic manner.

I've also made an explainer video on how to build a Julia Set. youtube.com/watch?v=5T0cC6KRezo This is actually more interesting than the Mandelbrot, because it can be thought of as a bunch of complex maps.

If your interested in how this is coded. I was chatting to Matt Henderson on Twitter (@matthen2) last night about this, and he showed me his "Shadertoy" version that he created independently. It's worth checking out if you have a mind for code (the code is much more elegant than my own): shadertoy.com/view/ws2cWt

Thank-you to my supporters on Patreon.

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Mapping a polar grid onto the Mandelbrot Set on iteration at a time.

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Mapping a polar grid onto the Mandelbrot Set on iteration at a time.