Maze DesignComputerbased maze design is a mix of techniques from discrete geometry and nonphotorealistic rendering. The twin questions of complexity and aesthetics in mazes both represent deep problems in computer graphics. 

Islamic star patternsTechniques for designing, rendering, and manufacturing Islamic star patterns, a traditional form of ornamentation that can be found across Europe, Asia, and Africa. 

EscherizationAn optimization process figures out how to deform an arbitrary shape to make it tile the plane, making it easier to produce new tessellations in the style of M.C. Escher. 
Patterns on surfacesA technique for decorating arbitrary mesh surfaces with ornamental patterns taken out of the plane. 

Metamorphoses and deformationsSome occasional work that encompasses Escher's use of the theme of metamorphosis, and the Parquet Deformations introduced by Huff and later popularized by Hofstadter. 

Fivefold tilingsI'm interested in the fivefold tiling problem, an open problem in tiling theory. The search for a solution produces many interesting and attractive tilings along the way. 

Aliasing ArtifactsVery simple programs can render rich and unexpected moire patterns. One especially surprising approach exposes lowlevel roundoff behaviour in the floating point unit. 

TSP ArtA form of halftoning in which an image is represented via a single, continuous closed path discovered as the (approximate) solution to an instance of the Traveling Salesman Problem. 

Near MissesA near miss is a polyhedron in which the faces are very nearly regular. The discrepancy is so small that you can probably build the polyhedron cleanly from paper using regular polygons. 

SymmetrohedraA simple construction based on finite symmetry groups yields a rich class of polyhedra containing many regular faces. A subset of a construction used later for Islamic star patterns. 

Voronoi ArtMany interesting ornamental designs can be constructed by computing the Voronoi diagrams of wellchosen arrangements of points. 
Ulam SpiralA few bits of math porn: pretty renderings of diagrams related to the Ulam spiral. 

Rotated Square IllusionA fun, abstracted image representation based on rotated, scaled squares. 

Hyperbolic SpidronsA short fantasy regarding the interpretation of abstract geometric spiral arrangements in hyperbolic geometry. 

My Funny ValentineAverage love (sorry if that sounds mean). 

Common Currency
I'm just a bill 
Craig S. Kaplan  Last updated: 