Vortices

Patterns and Simulations

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

Kleinian Group

Fractals and Chaos

The Ketoja-Satija Orchid

Fractals and Chaos

Singularity dynamics on fluid surface

Real Experiments

Singularity dynamics in curvature collapse and jet eruption on a fluid surface

Crack patterns

Real Experiments

Mud cracks when it shrinks and become brittle. If you make a uniform layer of mud and dry it uniformly, you get a pattern of irregular polygons with edges that usually meet at 90 degrees.