Any non-trivial property on CA is undecidable in any dimensions, IIRC you resort to Medvedev reducibility, oracles, etc... pretty quick with them. IMHO this is

Any non-trivial property on CA is undecidable in any dimensions, IIRC you resort to Medvedev reducibility, oracles, etc... pretty quick with them. IMHO this is semi interesting because having ANNs predict the outcome of deterministic dynamical systems may help with some planning tasks.