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Clayton Shonkwiler

Oof. Another one destroyed by over-aggressive video compression. See the source code link for a better version:


Voronoi diagram of stereographic projection of some spherical spirals.

Source code and slightly more explanation:

Our paper on the least symmetric triangle has been published by Geometriae Dedicata:

Here’s another fun image from the paper, which comes up in the course of determining the least symmetric acute triangle:

Small Changes

Stereographic projection of a Hamiltonian cycle on the great rhombicosidodecahedron.

Source code and more explanation:


Stereographic projection of points on the Clifford torus

Source code and more explanation:

Fall Out

Mapping a rotating circle on the sphere to the plane. Here's the map: first, send (almost every) point on the sphere to the point on the \(z=1\) plane contained in the same line through the origin. Then, invert the plane in the unit circle.

Source code:


A bunch of Brownian bridges approximating the unit circle.

(Not a GIF this time)


Stereographic projection (followed by orthogonal projection to the plane) of a flat torus in the 3-sphere.

Source code:


Stereographic projection of the latitude/longitude grid on the sphere.

Source code:


Take the square grid, inverse stereographic project to the sphere, then orthogonally project to the unit disk. Now, before mapping, translate the whole grid by \(-t(1,2)\) as \(t\) varies from \(-1\) to \(1\). This is the result.

Source code: