Big projects


Maze Design

Computer-based maze design is a mix of techniques from discrete geometry and non-photorealistic rendering. The twin questions of complexity and aesthetics in mazes both represent deep problems in computer graphics.


Islamic star patterns

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



An 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.

Smaller projects


Patterns on surfaces

A technique for decorating arbitrary mesh surfaces with ornamental patterns taken out of the plane.


Metamorphoses and deformations

Some 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 tilings

I'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 Artifacts

Very simple programs can render rich and unexpected moire patterns. One especially surprising approach exposes low-level round-off behaviour in the floating point unit.

[tsp art]


A 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 Misses

A 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.



A 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 art]

Voronoi Art

Many interesting ornamental designs can be constructed by computing the Voronoi diagrams of well-chosen arrangements of points.



Ulam Spiral

A few bits of math porn: pretty renderings of diagrams related to the Ulam spiral.


Rotated Square Illusion

A fun, abstracted image representation based on rotated, scaled squares.


Hyperbolic Spidrons

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


My Funny Valentine

Average love (sorry if that sounds mean).


Common Currency

I'm just a bill
Yes, I'm only a bill.

Craig S. Kaplan Last updated: