Bilinear fractal interpolation and box dimension

Abstract

In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read–Bajraktarevic operators. By exhibiting a generalized “taxi-cab” metric, we show that the graph of a bilinear fractal interpolant is the attractor of an underlying contractive bilinear IFS. We present an explicit formula for the box-counting dimension of the graph of a bilinear fractal interpolant in the case of equally spaced data points. Show more