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Since the introduction of strong anticipation by D.~Dubois the numerousinvestigations of concrete systems have been proposed. In proposed paper thenew examples of discrete dynamical systems with anticipation are considered.The mathematical formulation of problems, possible analytical formulas forsolutions and numerical examples of presumable solutions are proposed. One ofthe most interesting properties in such systems is presumable multivaluednessof the solutions. It can be considered from the point of view of dynamicalchaos and complex behavior. We represent examples of periodic and complexsolutions, attractor's properties and presumable applications inself-organization. The main peculiarity is the strong anticipation property.General new possibilities are the presumable multivaluedness of the dynamics ofautomata. Possible interpretations of such behavior of cellular automata arediscussed. Further prospects for development of automata theory and hypercomputation are proposed.

Multivaluedness Aspects in Self-organization, Complexity and Computations Investigations by Strong Anticipation