On star product fractal surfaces and their dimensions
type: Item
instance of: scholarly article
title: On star product fractal surfaces and their dimensions
zbMATH Open document ID: 0977.28006
DOI: 10.1007/BF02463785
author: Zhida Chen
author: He-Ping Xie
author: Zhigang Feng
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2001-07-18T00:00:00Z
review text: The author considers a fractal surface obtained by moving a fractal curve in the plane \(xOz\) along a curve in \(yOz\). This ruled surface \(F\) is called star product fractal surface and is formally defined by the equation \(z= f(x)+ g(y)- f(a)\), where \(x\in [a,b]\), \(y\in [c,d]\), and where \(f\) and \(g\) determine planar curves such that \(f(a)= g(c)\). The main aim of the paper is to show that the dimension of \(F\) equals one plus the maximum of the dimensions of the curves determined by \(f\) and \(g\).
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 1417779
zbMATH Keywords: fractal surface
zbMATH Keywords: fractal curve
zbMATH Keywords: dimension
reviewed by: Ilya S. Molchanov
MaRDI profile type: Publication
cites work: Some fractal models of fracture
cites work: Q4321769
cites work: Direct fractal measurement of fracture surfaces
description: scientific article; zbMATH DE number 1417779