V-variable fractals: Fractals with partial self similarity
2008 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 218, no 6, 2051-2088 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2008. Vol. 218, no 6, 2051-2088 p.
V-variable fractal, superfractal, fractal, random fractal, iterated function system, chaos game, Markov chain
IdentifiersURN: urn:nbn:se:uu:diva-109972DOI: 10.1016/j.aim.2008.04.011ISI: 000257807400012OAI: oai:DiVA.org:uu-109972DiVA: diva2:274916