Simulation of Diffusion on a Cellular Automaton in Two Dimensional Space

Authors: Mahmut EKEN, Şeref TURHAN, Nevzat AKTEKİN

Abstract: The non-equilibrium diffusion is simulated by using two dimensional square lattices with linear dimensions L=16, 32, 64, 128, 256. The cellular automaton rule is as follows: The system is completely empty at time t=0 except the source. The lattice which has at most one particle per site is divided into Margolus Blocks. For each iteration step a random number is generated, according to which each block is rotated clockwise or counterclockwise or stays immobile with equal probabilities and then it is shifted along a diagonal by a lattice constant. For each lattice we studied the percolation threshold p_c, the critical exponent, fractal dimension of the diffusion front D_f and other related quantities are computed. They are in agreement with the result of other simulation methods.