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An Overview of Evolutionary Cellular Automata Computation

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An Overview of Evolutionary Cellular Automata Computation

Scott McQuade

January 24, 2008

- 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.

- Objectives
- Methodology
- Results
- Interpretation of Results

- 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

- 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

- 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

- 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

- 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

- 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

- Simpler Strategy
- Works well with small or large ρ0

- Does not exhibit coordinated communication flow– processing done locally
- Does not scale well

- 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

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

- 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

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

- 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.