Sundial Mosaic

Patterns and Simulations

The image is created by iterating a map on a torus (the plane modulo a hexagonal lattice), counting the number of times each pixel is visited during the iteration, and coloring by number. (Poster for SIAM Journal on Applied Dynamical Systems.)

Fibres

Patterns and Simulations

Projection in R³ of a bundle of fibres in the complement of the trefoil knot in C², based on the dynamics of a set of matrices in SL[2,R].

Twisted Scroll Ring in Excitable Media

Patterns and Simulations

This image shows simulations of scroll-shaped waves often found in excitable media - such as heart tissue and chemical reactions.

Vortices

Patterns and Simulations

The dynamics of 6 randomly chosen vortices in an ideal fluid.