Cellular automata with pseudo-quantum evolution

A new approach to quantum phenomena is proposed. A serious defect of traditional quantum mechanics is the absence of trajectories for particles. Quantum theory gives a recipe only to calculate the probability amplitude for particle transition from initial state to final one. Probability amplitude (wave function) obeys local differential equation, but it's not a real physical field. The theory doesn't consider what happens during such a transition in the space-time. The measuring and the reduction don't enter explicitly in the model of a particle. A model of a simple world with an artificial particle with pseudo-quantum evolution is assumed. Pseudo-quantum evolution means only that a particle can be in a localized or in unlocalized states. Other properties of real particles are not assumed. The model includes a real (in this artificial world) field corresponding to the particle. The reduction enters the model explicitly. A new class of cellular automata that evolve in such a way is proposed.