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V-variable fractals: Fractals with partial self similarity

Barnsley, Michael; Hutchinson, John; Stenflo, Orjan


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 also be obtained from the points on the attractor of a single deterministic iterated function system. Existence, uniqueness and approximation results are established under average...[Show more]

CollectionsANU Research Publications
Date published: 2008
Type: Journal article
Source: Advances in Mathematics
DOI: 10.1016/j.aim.2008.04.011


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