Aperiodic and semi-periodic perfect maps

Paterson (see ibid., vol.40, p.743, 1993) has shown that the trivial necessary conditions are sufficient for the existence of a (binary) perfect map. These periodic structures can be transformed very simply into corresponding aperiodic and semi-periodic perfect maps. However, aperiodic and semi-periodic perfect maps can exist for parameter sets for which the corresponding periodic perfect maps cannot. In this paper it is shown, by construction, that (binary) aperiodic and semi-periodic perfect maps exist for all possible parameter sets.<
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