Abstract
We observe that there exists a natural homeomorphism between the attractors of any two iterated function systems, with coding maps, that have equivalent address structures. Then we show that a generalized Minkowski metric may be used to establish conditions under which an affine iterated function system is hyperbolic. We use these results to construct families of fractal homeomorphisms on a triangular subset of ℝ2. We also give conditions under which certain bilinear iterated function systems are hyperbolic and use them to generate families of homeomorphisms on the unit square. These families are associated with “tilings” of the unit square by fractal curves, some of whose box-counting dimensions can be given explicitly.
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Barnsley, M.F. (2009). Transformations Between Fractals. In: Bandt, C., Zähle, M., Mörters, P. (eds) Fractal Geometry and Stochastics IV. Progress in Probability, vol 61. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0030-9_8
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DOI: https://doi.org/10.1007/978-3-0346-0030-9_8
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