Abstract
Automatic sets are characterized by having a finite number of decimations. They are equivalently generated by fixed points of certain substitution systems, or by certain finite automata. As examples, two-dimensional versions of the Thue–Morse, Baum–Sweet, Rudin–Shapiro and paperfolding sequences are presented. We give a necessary and sufficient condition for an automatic set to be a Delone set in . The result is then extended to automatic sets that are defined as fixed points of certain substitutions. The morphology of automatic sets is discussed by means of examples.
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