The last domino falls: A little bit of science.
This paper and its deposited material explore clustering of 2 × 1 dimers (dominoes) subject to simple interactions and temperature. Much of the work in domino tilings has been statistical, combinatorial and thermodynamic in nature. Instead, here, the domino is used as a simple model of a non-spherical molecule to explore aggregation, rather as if the molecules were interacting in solution. As a result, the work does not look at how many ways there are to tile a plane, but at how the cluster evolves with different parameters in the potential that governs the clustering. These parameters include the rules used to select which of the many possible dominoes will be added to the cluster, and temperature. It is shown that qualitative changes in clustering behaviour occur with temperature, including affects on the shape of the cluster, vacancies and the domain structure.
The paper is on the web, open access, at http://dx.doi.org/10.3390/condmat2020015 and http://www.mdpi.com/2410-3896/2/2/15. It comes with a bundle of software anyone can use to play with the model, modify it, whatever. Please do!
It’s basically a toy model, but it shows some nice behaviour. Apologies to the red/green colour-blind.