V-variable fractals: fractals with partial self similarity

• Autores: Michael F. Barnsley, John E. Hutchinson
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 6, 2008, págs. 2051-2088
• Idioma: inglés
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• Resumen

  • 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.