A mathematical gallery

Many of the subjects I've worked on can be illustrated with nice pictures. Below is a collection of mathematical images related to papers I've written. See the references at the bottom for links to the relevant papers and additional information.

NEW (June 2016): I've created a web page about the moving sofa problem, which has additional fun mathematical pictures and animations.

1. A random square Young tableau of order 25, shown on the left as a discrete stepped surface. The smooth surface on the right is the limit shape of such random Young tableaux. The coloring scheme highlights the level curves of both surfaces. [References]
2. The half-way permutation of a random sorting network with 2000 particles. [References and movies]
3. A random domino tiling of the Aztec diamond of order 50. [References]
4. A random Erdos-Szekeres permutation of order 50, and the limit shape of such permutations, an algebraic curve of degree 4. [References]
5. Connectivity patterns in loop percolation on a cylinder. [References]
6. A fully packed loop configuration of order 8. [References]
7. Bootstrap percolation (picture by Alexander Holroyd). [References]
8. A tesselation of the hyperbolic plane by quadrilaterals. This is related to a natural dynamical system associated with Pythagorean triples. [References]
9. Limit shapes of bumping routes in the Robinson-Schensted correspondence. [References]

References

1. Random square Young tableaux

2. Random sorting networks

3. Domino tilings

4. Erdos-Szekeres permutations

5-6. Connectivity patterns in loop percolation, fully packed loops

7. Bootstrap percolation

8. Tesselation of the hyperbolic plane by quadrilaterals

9. Bumping routes in the Robinson-Schensted correspondence