J. Gorodkin, A. Sørensen, and O. Winther
Complex Systems 7, 1-23, 1993.
(Cover Illustration is from Figure 4.)
The genotype-phenotype relation for the 256 elementary cellular automata is
studied using neural networks. Neural network are trained to learn the
mapping from each genotype rule to its corresponding Li-Packard phenotype
class. By investigating learning curves and networks pruned with Optimal
Brain Damage on all 256 rules, we find that there is a correspondence between
the complexity of the phenotype class and the complexity (net size needed
and test error) of the net trained on the class. For Li-Packard Class A (null
rules) it is possible to extract a simple logical relation from the
pruned network. The observation that some rules are harder for the networks to
classify leads to an investigation of rule 73 and its conjugate rule 109.
Experiments reveal 3-cycles in magnetization in agreement with observations in
higher dimensional cellular automata systems.