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Journal Articles Journal of Physics A: Mathematical and Theoretical Year : 2009

Galton-Watson Iterated Function Systems

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Abstract

Iterated function systems (IFS) are interesting parametric models for generating fractal sets and functions. The general idea is to compress, deform and translate a given set or function with a collection of operators and to iterate the procedure. Under weak assumptions, IFS possess a unique fixed point which is in general fractal. IFS were introduced in a deterministic context, then were generalized to the random setting on abstract spaces in the early 1980 s. Their adaptation to random signals was carried out by Hutchinson and Rüschendorff [9] by considering random operators. This study extends their model with not only random operators but also a random underlying construction tree. We show that the corresponding IFS converges under certain hypothesis to a unique fractal fixed point. Properties of the fixed point are also described.

Dates and versions

hal-00367128 , version 1 (10-03-2009)

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Cite

Geoffrey Decrouez, Pierre-Olivier Amblard, Jean-Marc Brossier, Owen Jones. Galton-Watson Iterated Function Systems. Journal of Physics A: Mathematical and Theoretical, 2009, 42 (9), pp.095101. ⟨10.1088/1751-8113/42/9/095101⟩. ⟨hal-00367128⟩
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