To Appear in Proccedings of ANNIE-2002 1 FUZZY EVOLUTIONARY CELLULAR AUTOMATA J. NEAL RICHTER Department of Computer Science Utah State University Logan , Utah jnr@cc.usu.edu DAVID PEAK Department of Physics Utah State University Logan, Utah peakd@cc.usu.edu ABSTRACT An application of adaptive genetic algorithms to find optimal cellular automata rules to solve the density classification task is presented. A study of the statistical significance of previous results of the evolutionary cellular automata, EvCA, model is detailed, showing flaws in the fitness function. A brief review of recent work in advanced GAs and fuzzy-adaptive GAs is given. These techniques are then applied to the EvCA model to show improvement in convergence speed and more effective search of the optimization landscape. INTRODUCTION We reintroduce an application of genetic algorithms (GAs) to cellular automata., using the GA to evolve rules for performing global computations with simple localized rules. A new more accurate fitness function is introduced to compensate for inaccuracies in the old model. In addition, we extend the model to include fuzzy-logic-controlled GA parameter adaption EVOLUTIONARY CELLULAR AUTOMATA The EvCA group at the Santa Fe Institute has authored many papers on using the GA to evolve cellular automata (CA) rules to perform computation (Crutchfield et al., 1997 and Mitchell et al., 1993). The intent of the research was an initial step towards using GAs to enable decentralized computation in distributed multi-processor systems. Cellular automata are discrete space and time dynamical systems with localized parallel interaction. The universe of a CA is a grid of cells, where each cell can take on one of k states. The evolution of the CA in time is determined by a set of rules. See Wolfram (1994) for a more detailed background. The simplest form of a CA is a binary state, one-dimensional model where the current state of the space is defined by the binary states of the individual cells. At each time step, the state is formed by applying a set of transition rules to the previous state. The neighborhood r is the number of cells on either side of the current cell that affect the cell’s state in the next time step. The number of transition rules in such a system is defined as k 2r+1 . Figure 1 displays the k=2, r=1 CA system and table of 8 rules. This rule is refered to as Rule 90, the conversion of the 8 bit rule outputs into a decimal number. Figure 2 displays Rule 90 in action given a single cell on in the initial condition of the lattice.