Heesterbeek, J. A. P.; van Neerven, J. M. A. M.; Schellinx, H. A. J. M.; Zwaan, M. The nature of fractal geometry. (English) Zbl 0714.28006 CWI Q. 3, No. 2, 137-149 (1990). 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 Keywords:construction algorithms for fractal sets; Iterated Function Systems; invariant measure PDFBibTeX XMLCite \textit{J. A. P. Heesterbeek} et al., CWI Q. 3, No. 2, 137--149 (1990; Zbl 0714.28006)