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Published in:
Introduction to Fractals Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Measure Preserving Fractal Homeomorphisms

Authors : Michael F. Barnsley, Brendan Harding, Miroslav Rypka

Published in: Fractals, Wavelets, and their Applications

Publisher: Springer International Publishing

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Abstract

The basic theory of fractal transformations is recalled. For a fractal homeomorphism generated by a pair of affine iterated function systems (IFSs), a condition under which the transformation is measure (i.e. area, volume, etc.) preserving is established. Then three families of fractal homeomorphisms, two of them entirely new, generated by pairs of affine IFSs, are introduced. It is proved that they admit subfamilies that preserve n-dimensional Lebesque measure, where n is 2 or 3. Several examples are illustrated and applications to computer aided design and manufacture, via three-dimensional printing, are envisaged.

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previous chapter Parameter Planes for Complex Analytic Maps
next chapter The Dimension Theory of Almost Self-affine Sets and Measures
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Metadata
Title
Measure Preserving Fractal Homeomorphisms
Authors
Michael F. Barnsley
Brendan Harding
Miroslav Rypka
Copyright Year
2014
Book
Fractals, Wavelets, and their Applications

Print ISBN: 978-3-319-08104-5

Electronic ISBN: 978-3-319-08105-2

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-08105-2_5

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