Fractal geometry derived from complex bases
type: Item
instance of: scholarly article
title: Fractal geometry derived from complex bases
zbMATH Open document ID: 0493.10010
DOI: 10.1007/BF03023486
author: William J. Gilbert
published in: The Mathematical Intelligencer
publication date: 1982-01-01T00:00:00Z
review text: \textit{I. Kátai} and \textit{J. Szabó} [Acta Sci. Math. 37, 255--260 (1975; Zbl 0297.12003)] proved that every Gaussian integer can be represented uniquely in base \(b\) if \(b=-n \pm i\), where \(n\) is a positive integer and the digits in the representation are \(0,1,2,\ldots,n^2\). The author investigates the subsets of the Gaussian integers and complex numbers in which the numbers can be represented in some bases \(b\) (e.g. \(b= 1 - i)\). These subsets yield some intriguing geometric patterns in the complex plane, whose boundaries are fractal curves.
reviewed by: Péter Kiss
Mathematics Subject Classification ID: 11A63
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 3775616
zbMATH Keywords: Gaussian integers
zbMATH Keywords: representation
zbMATH Keywords: fractal curve
zbMATH Keywords: complex bases
MaRDI profile type: Publication
cites work: Q5859826
cites work: Q4745896
cites work: Q4050689
cites work: Q3935355
cites work: Q4131917
description: scientific article; zbMATH DE number 3775616