Emergence in the Game of Life
How do complex structures emerge from simple systems? How do you define emergence? Conway's Game of life is a popular and widely studied version of cellular automata. It is based on four simple rules for the evolution of a two-dimensional grid of squares that can either be dead or alive. What is amazing is that distinct patterns: still lifes, oscillators, and spaceships can emerge. Gosper's glider gun is shown below. What does this have to do with strongly correlated electron systems? The similarity is that one starts with extremely simple "rules" : a crystal structure plus Coloumb's law and the Schrodinger equation (Laughlin and Pines' Theory of Everything) and complex structures emerge: quasi-particles, broken symmetry states, topological order, non-Fermi liquids, ... Recently, Sophia Kivelson and Steven Kivelson [daughter and father] proposed the following definition: An emergent behavior of a physical system is a qualitative property that