Tuesday, October 16, 2018

Nested Spheres

This is a new shape that I have made based on sphere inversions. It is a nested set of spheres, such that each level of spheres is a Ford-Farey sphere packing over the Riemann sphere.

The structure is a tree, it has no self contact, but is also probably the densest packing that such a tree can be.
Each level is a graphical depiction of the Eistenstein rationals. So the total shape depicts an infinite cascade of Eisenstein rationals, rather like each nested sphere depicts the rationals over the infinitesimal gap that its parent sits on the complex plane. 

As such, one might describe it as a cascade-like depiction of the complex numbers.