On star product fractal surfaces and their dimensions (Q1970102)

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 \(g\).