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 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 contractive assumptions. We also obtain extensions of some basic results concerning iterated function systems.
Original language | English |
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Pages (from-to) | 2051-2088 |
Number of pages | 38 |
Journal | Advances in Mathematics |
Volume | 218 |
Issue number | 6 |
DOIs | |
Publication status | Published - 20 Aug 2008 |