An Overview of Evolutionary Cellular Automata Computation Scott McQuade January 24, 2008

A2 Papers J.P.Crutchfield and M.Mitchell. The evolution of emergent computation. PNAS, 92 (23): 10742, 1995. M.Mitchell, J.P.Crutchfield and R.Das. Evolving cellular automata to perform computations. In T. Back, D. Fogel, and Z. Michalewicz (editors), Handbook of Evolutionary Computation. Oxford: Oxford University Press, 1998.

Outline Objectives Methodology Results Interpretation of Results

Objectives Study the evolution and emergence of spatially extended, decentralized computing Occurs naturally (insect nests, aggregation of slime mold, parallel processing by sensory neurons, economical markets/pricing) (Crutchfield and Mitchell, 1995) Applications to computations systems Parallel Processing Lack of Central Processor More Efficient Communications

One-Dimensional Cellular Automata (Mitchell, Crutchfield, and Das, 1998)

Example Results (Mitchell, Crutchfield, and Das, 1998)

The Task Density Classification: If the initial configuration contains more 1’s than 0’s, all cells should eventually switch to 1’s If the initial configuration contains more 0’s than 1’s, all cells should eventually switch to 0’s This is referred to as the ρc=(1/2) Task ρ0 refers to the density of 1’s in the initial configuration

The Task No Cellular Automata can perform the ρc=(1/2) task perfectly across for all N Even for fixed N, a single cell, or a linear combination of cells, does not have the computation power to perform the ρc=(1/2) task well

Task Parameters N = 149 r = 3 2^7= 128 bit rule string; 2^128 possible rules ρ0 was uniformly distributed between 0 and 1 for the test cases NOT the unbiased distribution as it was too difficult Maximum Time of ~2N to produce the correct behavior

Basics of Genetic Algorithms Initial pool of algorithms or strategies Run all algorithms; Obtain results “Fitness Function” to evaluate the results of each existing algorithm Reproduction using the top performing algorithms– recombination (crossover) and mutation Repeat for multiple generations

GA Parameters The rules of the automaton will evolve, not the board itself 100 initial random rules (generated with “some initial biases”) Each rule evaluated on 100 uniformly distributed initial configurations (per generation) Fitness was the fraction of the 100 where correct behavior was produced For each generation Top 20 rules were retained Crossover of random pairings of the top 20 rules to produce the new 80 rules 2 random mutations per crossover 100 Generations

Results of Selected Rules (Crutchfield and Mitchell, 1995)

Block Expanding Rules (Mitchell, Crutchfield, and Das, 1998)

Block Expanding Rules Simpler Strategy Works well with small or large ρ0 Does not exhibit coordinated communication flow– processing done locally Does not scale well

Particle Based Rules (Mitchell, Crutchfield, and Das, 1998)

Particle Based Rules Complex patterns evolve Each “pattern region” (domain) can be classified and recognized be a DFA The constant patterns can be filtered out, leaving only the boundaries between domains These domain boundaries act like particles, travelling at constant velocities and interacting with each other

Particle Based Rules (Crutchfield and Mitchell, 1995)

Particle Based Rules (Crutchfield and Mitchell, 1995)

Synchronization Task (Mitchell, Crutchfield, and Das, 1998)

Conclusions Complex particle-based rules evolved infrequently but consistently (7 out of 300 runs) The evolution consisted of distinct epochs with distinct innovations

Conclusions Using an unbiased initial configuration (ρ0 ≈ ½), was too difficult for initial generations A uniform [0, 1] ρ0 distribution was used, but this proved to be too easy in later generations The authors mentioned the possibility of a co-evolution sheme Breaking of symmetries proved to be a problem

Conclusions Possible applications to more complex real-world problems (image processing) Insight into natural evolutionary behavior

References 1. J.P.Crutchfield and M.Mitchell. The evolution of emergent computation. PNAS, 92 (23): 10742, 1995. 2. M.Mitchell, J.P.Crutchfield and R.Das. Evolving cellular automata to perform computations. In T. Back, D. Fogel, and Z. Michalewicz (editors), Handbook of Evolutionary Computation. Oxford: Oxford University Press, 1998.