In general, aesthetic beauty is a notoriously hard notion to define and certainly depends a lot on subjective tastes. However, there are certain attributes which do seem to be common, underlying themes in universal ideas of beauty. Some of these attributes include symmetry, simplicity, and tension between order and disorder. As a physicist, much of what I intuitively see as beautiful in nature can be traced to the occurrence of these properties in the mathematics of our models of reality; symmetries in the quantum field theory Lagrangians of particle physics, simplicity in the least action principles of classical physics, and the tension between order and disorder in statistical mechanics phase transitions. As an artist, I try to illustrate these ideas through the direct visual impact of the work as well as through the mathematical subject matter. On a lighter note, playing around with math, physics, and art is just plain fun!
The coloration on this egg was produced by dyeing with successively darker dyes and blocking off areas with bees wax between applications. The surface is broken up into 48 red and black triangles, which are formed from the intersection of 8 great circles (if this were a sphere). The black triangles contain a trefoil knot (left-handed), which is the first non-trivial prime knot and the (2,3)-torus knot. The red triangles contain a link usually referred to as Borromean rings. They have the interesting property that cutting one loop will release the other two.
The outer region has a traditional Islamic tessellation of the plane, while the inner region consists of seven Japanese inspired patterns. This inner region can be considered the fundamental domain of the universal cover of the torus, i.e. you can connect the top edge to the bottom and then the left edge to the right to form the surface of a doughnut. On the torus the seven patterns, or colors, form contiguous regions, each of which touch every other color. On the plane, such a partitioning of the space would need at most four colors to distinguish the regions. On a torus, seven colors are sufficient; indeed, I've illustrated a case where all seven colors are needed.