Determining the critical temperature of the continuous-state game of life

Abstract

This paper proposes a simple algorithm to find the critical temperature of the continuous-state Game of Life (GoL). The algorithm conducts the transitions of cells and the update of the temperature parameter alternatingly. The temperature starts from a low value and it increases gradually, while a fixed GoL pattern evolves. This process continues, but before the temperature exceeds the critical temperature, the update algorithm acts to decrease it, so as to prevent overshoot of the temperature, which would make the cell states deviate from the normal GoL behavior. An oscillatory value of the temperature can be observed, but it converges towards a fixed value, indicating that its critical point is being approached. © 2012 Springer-Verlag Berlin Heidelberg.