A Mandelbrot set for pairs of linear maps
type: Item
instance of: scholarly article
title: A Mandelbrot set for pairs of linear maps
zbMATH Open document ID: 0582.58023
DOI: 10.1016/S0167-2789(85)80008-7
author: M. E. Barnsley
author: Andrew N. Harrington
published in: Physica D
publication date: 1985-01-01T00:00:00Z
review text: The set of points \(A(s)=\{\pm 1\pm s\pm s^ 2\pm s^ 3\pm..\). for all sequences of \(+\) and -\(\}\), where \(s\in {\mathbb{C}}\) and \(| s| <1\), is generically a fractal. For example A(1/3) is the classical Cantor set and \(A(1/2+i/2)\) is a dragon curve. This set of fractals can be classified in terms of an associated Mandelbrod set \(D=\{s\in {\mathbb{C}}:\) \(| s| <1\), A(s) is disconnected\(\}\). The structure of D and its boundary are investigated.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 3932054
zbMATH Keywords: set of fractals
zbMATH Keywords: Mandelbrod set
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3932054