# Charles G. Gunn

I enjoy the process of generating images embodying formal properties in a sensual form. Although I like to think of myself as a generalist, I have a special affinity for discrete groups, noneuclidean geometry, projective geometry, and cellular automata, with a special love for forgotten 19th century mathematics. Once I have everything set up in terms of the formal mathematical/programmatic basis (I roll most of my own software partly because there isn't any alternative and partly because I like to have total control), I just play with the software. I particularly enjoy encountering unexpected results, whether they be mathematical or aesthetic, since they often lead to new connections.

The 10-cell is a regular tessellation of the three-dimensional sphere by 10 identical truncated tetrahedra (TT). Its rich and complex symmetry is portrayed in this image. The image was rendered using curvilinear perspective (see C. Gunn, "Rendering the Whole World ...", Bridges 2013) to obtain a conformal image in which all 10 TTs are visible. Each TT is paired with its polar partner in the same color. The 10 circles are the axes of screw motions preserving the 10-cell, generating the symmetry group of the 10-cell. The 2-color stripe on each circle identifies which TTs it meets, and the twisting of the stripe shows how the screw motion rotates while it translates.

All these black and white images have the same symmetry group (22X in the Conway-Thurston orbifold notation) and were generated algorithmically using a Turing reaction-diffusion process with custom software that respects the symmetry group (extending work of Jonathon McCabe, "Cyclic Symmetric Multi-Scale Turing Pattern", Bridges 2010). I've combined them into a single image to highlight how, despite the strict "rules of the game", a colorful variety of moods and gestures are still possible: abstract and formal, dynamic, humorous, plant-like, etc. The element of symmetry heightens the visual charm through surprising "self-encounters" of the basic shapes, as does the possibility of shifting one's focus between black and white forms.