Can quantum mechanics be reconciled with cellular automata?

After a brief account of the GHZ version of the Bell inequalities, we indicate how fermionic fields can emerge in a description of statistical features in cellular automata. In square lattices, rotations over arbitrary angles can be formulated in terms of such fields, but it will be difficult to produce models with exact rotational invariance. Symmetries such as rotational symmetry will have to be central in attempts to produce realistic models.