F von Haeseler

Correlation and Spectral Properties of Multidimensional Thue-Morse Sequences

This paper considers higher-dimensional generalizations of the classical one-dimensional two-automatic Thue–Morse sequence on ℕ. This is done by taking the same automaton-structure as in the one-di...

Limit sets of automatic sequences

Abstract We show that for every k-automatic sequence there exists a natural number p>0 such that the sequences of the form (kpn+j)n⩾0 with j=0,…,p−1 are scaling sequences for f. Moreover, we demonstrate that every limit set is the union of certain basic limit sets.

Correlation functions of higher-dimensional automatic sequences

A procedure for calculating the (auto)correlation function , of an m-dimensional complex-valued automatic sequence , is presented. This is done by deriving a recursion for the vector correlation function Γker(f)(k) whose components are the (cross)correlation functions between all sequences in the finite set ker(f), the so-called kernel of f which contains all properly defined decimations of f. The existence of Γker(f)(k), which is defined as a limit, for all , is shown to depend only on the existence of Γker(f)(0). This is illustrated for the higher-dimensional Thue–Morse, paper folding and Rudin–Shapiro sequences.

Cellular automata, quasigroups and symmetries

Summary. We investigate cellular automata (CA) with a local rule

Correlation and spectral properties of higher-dimensional paperfolding and Rudin?Shapiro sequences

\phi : G^2 \rightarrow G

Automatic sets and Delone sets

, where the local rule defines a quasigroup structure (Latin square) on the finite set G. If the quasigroup is semisymmetric or totally symmetric, some top-down equilateral triangular subsets of the CA-orbits, the so-called

Scaling properties of generalized Carlitz sequences of polynomials

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Averages of automatic sequences

-configurations, exhibit certain symmetries. The most interesting symmetries are the rotational and the total (dihedral) symmetries, which may be considered in conjunction with certain automorphisms.¶We first explore the conditions for quasigroups to be symmetric (or for local CA-rules to allow symmetric

The Pascal matroid as a home for generating sets of cellular automata configurations defined by quasigroups

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GENERALIZED DECIMATION INVARIANT SEQUENCES IN DIMENSION N

-configurations), and how to construct symmetric quasigroups by prolongation, i.e., by steadily increasing the order of the quasigroup, thereby conserving the symmetry. Then we study rotationally or totally symmetric