Functional Information of a Driven Cellular Automaton

For decades cellular automata (CA) simulations have proven versatile in modeling a wide range of complex natural phenomena due to their limited dimensionality and ability to allow adjustment of the small number of parameters that control self-organization. In this study, a model was designed that extends the self-organized phase of an automaton by keeping a single cell in a permanently (perennial) active state. After interacting with over 400,000 initial configurations of randomly placed standard automata cells surrounding the perennial cell, hundreds of unique and geometrically complex stable structures were created by the end state of evolution. These structures are analyzed with the goal of quantifying their complexity beyond the expected selection bias inherent in CA. A correlation was established between the average number of of generations required to construct each structure and its complexity as measured by functional information theory. This link between information measured in bits and construction in generations quantifies the computational work performed by the state transition rule of the CA. Because complexity is frequently in the eye of the beholder, the correlations developed in this work remove observer bias from the often-difficult task of defining complexity generated by self-organized processes in nature.