# Clayton Shonkwiler

I am inspired by the beautiful mathematics that arise in my research and teaching. Whereas in research the challenge is often to translate intuition into new and useful mathematics, with my art the goal is very nearly the opposite: to translate known mathematics into (aesthetically pleasing) intuition.

The orbit of a point in the Poincaré disk model of the hyperbolic plane under the action of the modular group, shown to the first few levels of the Cayley graph of a particular presentation of the modular group.

Applying the Möbius transformation sending the upper half-plane model of the hyperbolic plane to the Poincaré disk model to this animation yields a simple rotation of the square-grid circle packing around a central circle. In this sense, the animation shows a hyperbolic rotation of a circle packing.