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arXiv · 0802.0064

V-Variable Fractals: Fractals with Partial Self Similarity

Michael Barnsley·John E. Hutchinson·Örjan Stenflo
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Abstract

We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a corresponding class of V-variable fractal sets or measures. These V-variable fractals can be obtained from the points on the attractor of a single deterministic iterated function system. Existence, uniqueness and approximation results are established under average contractive assumptions. We also obtain extensions of some basic results concerning iterated function systems.

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Michael Barnsley, John E. Hutchinson, Örjan Stenflo. 2008-02-01. V-Variable Fractals: Fractals with Partial Self Similarity. https://arxiv.org/abs/0802.0064

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