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.
A large uniformly random tiling of the Aztec diamond displaying the artic circle phenomenon
A mild inhomogeneity in the weights leads to a cardioid arctic curve
Another choice of inhomogeneity leads asymptotically to a tacnode
Some judicious choice of null weights leads to the joining of two semi-standard Young tableaux of conjugate shapes
The same as above but with a mixed middle
Same as above but with a randomly frozen middle
A uniform tiling of a partial (half the) Aztec diamond with prescribed middle
A random domino tiling of a square...
... obtained by sampling a tiling of the Aztec diamond with frozen extremities
Some waterfalls (spaghetti)