Computational Modelling Group

Renormalisation of 2D cellular automata with an absorbing state

Adam Prugel-Bennett, Iain Weaver

A model of directed percolation initialised from a single seed in 2+1 dimensions shown here above the critical point, where clusters grow and percolate through time. (left) represents the process in 3 dimensions while (right) shows cross-sections at diffe

We describe a real-space renormalisation scheme for non-equilibrium probablistic cellular automata (PCA) models, and apply it to a two-dimensional binary PCA. An exact renormalisation scheme is rare, and therefore we provide a method for computing the stationary probability distribution of states for such models with which to weight the renormalisation, effectively minimising the error in the scale transformation.


Programming languages and libraries: C, Mathematica, Matlab

Transdisciplinary tags: Complex Systems, Computer Science