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Bilinear Fractal Interpolation and Box Dimension

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.

preprint2014arXivOpen access
Michael F. BarnsleyPeter R. Massopust
math.MG
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Michael F. BarnsleyPeter R. Massopust

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