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DIMENSIONS OF SELF-AFFINE FRACTALS AND MULTIFRACTALS GENERATED BY UPPER-TRIANGULAR MATRICES

KENNETH FALCONER

Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, United Kingdom

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and

JUN MIAO

Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, United Kingdom

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https://doi.org/10.1142/S0218348X07003587Cited by:36 (Source: Crossref)

Abstract

We consider calculation of the dimensions of self-affine fractals and multifractals that are the attractors of iterated function systems specified in terms of upper-triangular matrices. Using methods from linear algebra, we obtain explicit formulae for the dimensions that are valid in many cases.

Keywords:

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