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The nature of fractal geometry. (English) Zbl 0714.28006

Author’s abstract: In this paper two well-known construction algorithms for fractal sets, based on Iterated Function Systems, are discussed and their mathematical justification is given. It is shown that both the Deterministic and the Random construction yield the same fractal sets. In the former case the fractal set arises as the limit of a Cauchy sequence of compact sets, in the latter case it appears as an invariant measure. Sufficient conditions are given such that for a measure \(\lambda\) there exists an Iterated Function System with probabilities that has an associated invariant measure equal to \(\lambda\).
Reviewer: G.Keller

MSC:

28A80 Fractals
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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