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Bilinear fractal interpolation and box dimension

Barnsley, Michael F.; Massopust, Peter R.

Description

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.

CollectionsANU Research Publications
Date published: 2015-11-06
Type: Journal article
URI: http://hdl.handle.net/1885/12859
Source: Journal of Approximation Theory
DOI: 10.1016/j.jat.2014.10.014

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