ITEM METADATA RECORD
Title: Automatic sets and Delone sets
Authors: BarbĂ©, AndrĂ© ×
von Haeseler, F #
Issue Date: Apr-2004
Publisher: Iop publishing ltd
Series Title: Journal of Physics A. Mathematical and General vol:37 issue:13 pages:4017-4038
Abstract: Automatic sets D subset of Z(m) 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 D subset of Z(m) to be a Delone set in R-m. 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.
URI: 
ISSN: 0305-4470
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
× corresponding author
# (joint) last author

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