  To test generalization ability of a class of deep neural networks, we
randomly generate a large number of different rule sets for 2-D cellular
automata (CA), based on John Conway's Game of Life. Using these rules, we
compute several trajectories for each CA instance. A deep convolutional
encoder-decoder network with short and long range skip connections is trained
on various generated CA trajectories to predict the next CA state given its
previous states. Results show that the network is able to learn the rules of
various, complex cellular automata and generalize to unseen configurations. To
some extent, the network shows generalization to rule sets and neighborhood
sizes that were not seen during the training at all.
