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Mathematics is a place where you can do things which you can’t do in the real world (Marcus Du Sautoy, mathematician)

From time to time I have a look to some of my previous posts: it’s like seeing them through another’s eyes. One of my first posts was this one, where I draw fractals using the Multiple Reduction Copy Machine (MRCM) algorithm. That time I was not clever enough to write an efficient code able generate deep fractals. Now I am pretty sure I could do it using ggplot and I started to do it when I come across with the idea of mixing this kind of fractal patterns with Voronoi tessellations, that I have explored in some of my previous posts, like this one. Mixing both techniques, the mandalas appeared.

I will not explain in depth the mathematics behind this patterns. I will just give a brief explanation:

I start obtaining n equidistant points in a unit circle centered in (0,0)

I repeat the process with all these points, obtaining again n points around each of them; the radius is scaled by a factor

I discard the previous (parent) n points

I repeat these steps iteratively. If I start with n points and iterate k times, at the end I obtain n^{k} points. After that, I calculate the Voronoi tesselation of them, which I represent with ggplot.