Spheres of Wada

Wada basins, approximated using spheres and raytracing.


I saw this post on Hacker News and, much like the first commenter, had a hard time grasping what the wikipedia page was saying. But I stumbled upon this explanation page in the Wikipedia sources.

I reproduced that sphere setup in Blender and used the SheepIt render farm to render it in only a few minutes.

If you, like I, have a difficult time understanding how that simple geometry induces a fractal pattern in reflection, then perhaps this video will help you.

Throw a colored blanket over three of the four holes when you stack four spheres, and stick your eye in the last hole. Wada.

The phenomenon you see here is that of the three colors (R/G/B) visible in the reflections, each point along the boundary of each colored area touches at least one red, one blue, and one green region each.

(In cases where this falls apart in my visualization, it is not a failure of the property: It is a shortcoming of my raytracer, which only bounces a few dozen times and so doesn’t reflect the full fractal geometry on display in a mathematical model version.)

Written on October 8, 2018