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Von Koch and Thue-Morse revisited J.-P. Allouche
 

Summary: Von Koch and Thue-Morse revisited
J.-P. Allouche
CNRS, LRI
B^atiment 490
F-91405 Orsay Cedex (France)
allouche@lri.fr
G. Skordev
CEVIS, Universit¨at Bremen
Universit¨atsallee 29
D-28359 Bremen (Germany)
skordev@cevis.uni-bremen.de
Abstract
We revisit the relation between the von Koch curve and the Thue-Morse sequence
given in a recent paper of Ma and Goldener by relating their study to papers written by
Coquet and Dekking at the beginning of the 80's. We also emphasize that more general
links between fractal objects and automatic sequences can be found in the literature.
1 Introduction
The recent paper of Ma and Holdener [27] gives an interesting explicit relation between the
von Koch curve and the Thue-Morse sequence. We show here that such a link was already
noted in two papers dated 1982­1983, one by Coquet [8] (where the name "von Koch" is

  

Source: Allouche, Jean-Paul - Laboratoire de Recherche en Informatique, Université de Paris-Sud 11

 

Collections: Computer Technologies and Information Sciences