This simulation demonstrates double dimer configurations on an Aztec diamond. Two independent dimer configurations are sampled and displayed simultaneously - one in black and one in red. The simulation uses random IID weights sampled from either a Bernoulli distribution or a log-normal distribution (exp(β × X) where X ~ N(0,1)) to generate tilings via the shuffling algorithm. The original python code was created by Sunil Chhita; this version is adapted for JS + WebAssembly. Visualization is done using D3.js.

The sampler works in your browser. Up to $n \sim 120$ it works in reasonable time, but for larger $n$ it may take a while. I set the upper bound at $n=400$ to avoid freezing your browser.

Random Weights: Each edge weight $W_{ij}$ is sampled independently from one of three distributions:

• Bernoulli: Takes value “Value 1” with probability “P(Value 1)” and value “Value 2” with probability $1 - P(\text{Value 1})$. The default values (1/2 and 3/2 with equal probability) create a mildly inhomogeneous environment.
• Gaussian: $W_{ij} = e^{\beta X_{ij}}$ where $X_{ij} \sim N(0,1)$ are independent standard normal random variables. The parameter $\beta$ controls the variance of the log-weights.
• Gamma: $W_{ij} = \text{Gamma}(\alpha, 1)$ for some of the edges (even rows, i.e., $i$ even), and $W_{ij} = 1$ for other edges (odd rows, i.e., $i$ odd). The shape parameter $\alpha$ controls the distribution of the gamma weights.

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code

(note: parameters in the code might differ from the ones in simulation results below)

• Link to code (This simulation is interactive, written in JavaScript, see the source code of this page at the link)
• Link to code (C++ code for the simulation)

Dear colleagues:

Feel free to use code (unless otherwise specified next to the corresponding link), data, and visualizations to illustrate your research in talks and papers, with attribution (CC BY-SA 4.0). Some images are available in very high resolution upon request. I can also produce other simulations upon request - email me at lenia.petrov@gmail.com