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Quasi-Linear Transformations, Numeration Systems and Fractals

  • Marie-Andrée Jacob-Da Col
  • Pierre Tellier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6607)

Abstract

In this paper we will define relations between quasi-linear transformations, numeration systems and fractals. A Quasi-Linear Transformation (QLT) is a transformation on \(\mathbb Z^n\) which corresponds to the composition of a linear transformation with an integer part function. We will first give some theoretical results about QLTs. We will then point out relations between QLTs, numeration systems and fractals. These relations allow us to define new numeration systems, fractals associated with them and n-dimensional fractals. With help of some properties of the QLTs we can give the fractal dimension of these fractals.

Keywords

Gaussian integers algebraic integers numeration systems discrete linear transformations fractals 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Marie-Andrée Jacob-Da Col
    • 1
  • Pierre Tellier
    • 1
  1. 1.LSIIT-UMR 7005Pôle APIIllkirch CedexFrance

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