Multidimensional East model simulation
Published:
The model
The East model is an interacting particle system on the \(0-1\) state space. If either the south or west neighbour is in state \(0\) at the time of a ring, a vertex can update with the equilibrium distribution given locally by \(\mathrm{Bernoulli}(1-q)\) where \(q\) is a parameter of the model and corresponds to the density of \(0\) states. The vertex ring at the origin is always unconstrained and we start the model from the state with only \(1\)s.
The primary problem we try to solve in my paper with Fabio Martinelli is trying to find front evolution speeds in different directions.
The code
The code base consists of two independent simple simulations written in Python.
In east_front.py I concurrently calculate many independent East process evolutions and analyse the front evolution along the diagonal and along the axes and calculate an average of that time. It should be clear from the above video that these are very different times and we used the simulation to confirm the order of magnitude in which these times should differ.
In east_front_plot.py I simulate a single East evolution and in specific intervals save the state to an image which results in the above video and also in the picture of the final state included in the paper.