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The chaos game on a general iterated function system. (English) Zbl 1221.37079

The authors prove that, under fairly general hypotheses, the chaos game algorithm applied to iterated function systems, almost always yields an attractor.

MSC:

37D99 Dynamical systems with hyperbolic behavior
28A78 Hausdorff and packing measures

References:

[1] Jaroszewska, Univ. Iagel. Acta Math. 40 pp 137– (2002)
[2] DOI: 10.1017/S0143385700004168 · Zbl 0621.60039 · doi:10.1017/S0143385700004168
[3] DOI: 10.1080/00207210500171620 · Zbl 1087.37013 · doi:10.1080/00207210500171620
[4] DOI: 10.1137/1034082 · Zbl 0759.58021 · doi:10.1137/1034082
[5] Barnsley, Ann. Inst. H. Poincaré 24 pp 367– (1988)
[6] DOI: 10.1017/S0143385798108271 · Zbl 0940.60014 · doi:10.1017/S0143385798108271
[7] Barnsley, Fractals Everywhere (1988)
[8] DOI: 10.1088/0951-7715/17/6/016 · Zbl 1100.60039 · doi:10.1088/0951-7715/17/6/016
[9] Stenflo, Fractals in Multimedia (2002)
[10] Onicescu, Bull. Sci. Math. France 59 pp 174– (1935)
[11] Leśniak, Math. Slovaca 53 pp 393– (2003)
[12] DOI: 10.1098/rspa.1985.0057 · Zbl 0588.28002 · doi:10.1098/rspa.1985.0057
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