The gap between IFS attractor and strictly self-similar set

Tianjia Ni and Zhiying Wen

Chaos, Solitons & Fractals, 2025, vol. 200, issue P1

Abstract: An IFS (Iterated Function System) attractor is the unique invariant set of a family of contractions, and a strictly self-similar set is the unique invariant set of a family of similitudes. Any strictly self-similar set is automatically an IFS attractor by definition. For the inverse direction, although the discrepancy between the two concepts is subtle, we herein present a surprising example of an IFS attractor K such that there is no strictly self-similar set possessing the same self-similar topological structure as K.

Keywords: Self-similar set; IFS attractor; Quotient space; Metrization (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:200:y:2025:i:p1:s0960077925009725

DOI: 10.1016/j.chaos.2025.116959

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