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–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.
|Collections||ANU Research Publications|
|Source:||Journal of Approximation Theory|
|Barnsley and Massopust Bilinear Fractal Interpolation 2015.pdf||379.98 kB||Adobe PDF|
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