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

2. 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.

3. Outline
Objectives
Methodology
Results
Interpretation of Results

4. 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

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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. Results of Selected Rules (Crutchfield and Mitchell, 1995)

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

14. 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

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

16. 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

17. Particle Based Rules (Crutchfield and Mitchell, 1995)

18. Particle Based Rules (Crutchfield and Mitchell, 1995)

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

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

21. 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

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

23. 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.