Bilinear Fractal Interpolation and Box Dimension

2012/09/14 by Barnsley, Michael F., Massopust, Peter R. · 1 citation
#28A80 #37L30 #41A05 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1209.3139

Abstract

In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarević 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.

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