Self-similarity
type: Item
instance of: scholarly article
title: Self-similarity
zbMATH Open document ID: 0806.58033
author: Gary B. Lewellen
published in: Rocky Mountain Journal of Mathematics
publication date: 1995-02-16T00:00:00Z
review text: Self-similarity has been treated recently in connection with the study of fractals; so the paper seems to be very actual. In Section 1 a self- similar set is defined as a compact set which is the union of its images under members of a collection of contractions (indexed by a compact set) having a common contradictivity factor. In Section 2 self-similarity is characterized ``addressing'' or considering points in the self-similar set as limits associated with certain sequences of contractions. The existence of self-similar sets determined by a collection of a certain type of contractions is proved in Section 3. A self-similar set is treated in Section 4 as a fixed point in hyperspaces and the continuous variation of self-similar sets is shown in the last Section 5. In the Introduction a short historical review is presented.
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 51M05
Mathematics Subject Classification ID: 54B20
zbMATH DE Number: 515171
zbMATH Keywords: self-similarity
zbMATH Keywords: contraction
zbMATH Keywords: addressing
reviewed by: Andrzej Pelczar
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072539
OpenAlex ID: W4237205815
cites work: Q4040874
cites work: Iterated function systems and the global construction of fractals
cites work: On the structure of self-similar sets
cites work: Q3731958
cites work: Q3220809
cites work: On the quadratic mapping \(z\rightarrow z^{2}-\mu \) for complex \(\mu \) and \(z\): the fractal structure of its set, and scaling
cites work: Composition of contractions
DOI: 10.1216/RMJM/1181072539
description: scientific article; zbMATH DE number 515171