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

2. Rewarding Complex Behavior During Computation Speeds Evolution

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

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

5. Time-Space Diagram of CA

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

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

8. 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

9. Generations to High Performance n = 72

10. 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.