# Ian Sammis

Creating mathematical art gives me a wonderful excuse to explore parts of mathematics well outside my specialty. The effort to make a mathematical idea aesthetically pleasing forces me to understand the underlying mathematics differently and more completely than I otherwise would.

A Sierpinksi curve is a space-filling curve that fills a triangle. Sierpinski curves may be chained together to construct a continuous path from triangle to triangle. The correct arrangement of triangles allow the construction of a single path that fills the unit square while following an Eulerian path along a graph with the topology of a torus. Mapping the square onto the torus in the usual way gives us a space-filling closed circuit on the surface of a torus. The image is a render of a tube following such a circuit.