Dan Betea - Simulations

Some large random objects

Here you'll find a few large random tilings or other objects, randomly sampled according to some "natural" distribution, using a variety of sampling techniques and languages (Python+sage, C/C++, Java). More details are coming as soon as Google Sites makes allowances for mathematical typesetting.

This page is permanently under construction as new material is added. I hope to post some of the code that generated these on my GitHub page at some point.

Pyramid partitions (and related)

A random volume (flip) weighted tiling of the upper half plane by dominoes, see here

The same object from above, but now as a stack of cubes called a strict plane partition

A random volume weighted domino tiling of the whole plane, a pyramid partition

A random volume weighted domino of a planar strip, a restricted pyramid partition

Phenomena inside the Aztec diamond

What follow are random tilings of Aztec diamonds under various and mostly inhomogeneous measures. See this page of A. Borodin and M. Borodin for 3D representations, further mathematical explanations and references; and this page (by the same authors) for an introduction.