NECESSITY FROM CHANCE: SELF-ORGANIZED REPLICATION OF SYMMETRIC PATTERNS THROUGH SYMMETRIC RANDOM INTERACTIONS

Abstract

We present an algorithm, completely random in nature, that, without invoking a fitness function or purposeful design, produces symmetric replicas in a population of so-called cellicules. Cellicules consist of "cells" arranged in a structure with geometric symmetry S. Each cell has one of two possible states, thus defining a state-configuration pattern on a cellicule. The algorithm acts recurrently on a population of cellicules, possibly randomly initialized, through a random "copying interaction" between two randomly selected cellicules that first undergo a random reorientation in accordance with the symmetry S. The dynamics of the algorithm is analyzed in detail for several symmetries. This shows that it is a random walk with absorbing states which correspond to a population in which all cellicules have an identical S-symmetric configuration pattern. We discuss some aspects concerning the evolution of cellicule-populations under mixing and mutation, and some variations on the basic algorithm.