CS267 Final Project: Isles of Eden

Cellular Automata are mathematical representations of physical systems which can be described as a regular uniform lattice with discrete variables at each cell represented by 0 or 1. The state of the cell is determined by its neighbors at each time step according to a set of local rules. From these simple set up rules, complex behavior can appear. These systems have been simulated in many different context from games like The Game of Life, random number generators such as Wolfram Mathematica, and in real life patterns such as certain seashells. Our project is an attempt to parallelize the detection of certain behaviors of a 1-D cellular automata. In particular, we have focused on finding the Isles of Eden. An Isle of Eden is an input that, under several time steps, will return to its original state. In other words, some patterns generate a steady state period, so called Period N Isles of Eden. Some of these can be easily recognized in the Game of Life as the common blinkers and pulsars. Other patterns exist such as Attractors, which are steady states that many other initial inputs will collapse to, and Gardens of Eden, inputs that can never be recovered after one time step. The 1-D cellular automata is described by an input bit string, and a rule composed of a combination of bit shifts and logical bit operations. We used Rule 150, which contains all Isles of Edens for bit lengths not multiples of 3, and Attractors otherwise. Rule 150 is described by: