  Cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics
are its ontological states that evolve by permutations, in this way never
creating would-be quantum mechanical superposition states. We review and
illustrate this with a classical Ising spin chain. It is shown that it can be
related to the Weyl equation in the continuum limit. Yet, the model of discrete
spins or bits unavoidably becomes a model of qubits by generating
superpositions, if only slightly deformed. We study modifications of its signal
velocity which, however, do not relate to mass terms. To incorporate the
latter, we consider the Dirac equation in 1+1 dimensions and sketch an
underlying discrete deterministic "necklace of necklaces" automaton that
qualifies as ontological.
