On star product fractal surfaces and their dimensions
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 \(g\).
scientific article; zbMATH DE number 1417779