Complexity as Fitness for Evolved Cellular Automata Update Rules Em Ward, Douglas S. Blank, Douglas Rolniak, and Dale R. Thompson University of Arkansas, USA

Rewarding Complex Behavior During Computation Speeds Evolution

The Computation Cellular Automaton (CA) solution of the binary density-classification task Update rules evolved with genetic algorithm (GA)

The Density Classification Task Rule Table Cellular Automata Neighborhood Output 000 001 010 011 1 100 101 110 111 ••• 1 ••• 1 •••

Time-Space Diagram of CA

Complex Behavior of CA Propagating, localized structures May be long-lived “long transients” Required for computation

Capturing Complex Behavior Areas of low and high state change frequency Long structure (exists over many time steps)

Analysis Parameters ω captures areas of low and high state-change frequency “good” rules have higher ω than “bad” and random rules (p<0.001) jot captures long transient

Generations to High Performance n = 72

Conclusions Complex behavior during computation can be captured by numerical markers. Incorporation of markers into fitness function for genetic algorithm CA update rules speeds evolution. http://csce.uark.edu/ai/