Bilinear fractal interpolation and box dimension

• Michael F. Barnsley ^[1] ; Peter R. Massopust ^[2]
  1. [1] Australian National University

     Australian National University

     Australia

     
  2. [2] Technical University Munich

     Technical University Munich

     Kreisfreie Stadt München, Alemania

     
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 192, Nº 1 (April 2015), 2015, págs. 362-378
• Idioma: inglés
• DOI: 10.1016/j.jat.2014.10.014
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• Resumen

  • 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.