Bilinear fractal interpolation and box dimension

@article{Barnsley2012BilinearFI,
  title={Bilinear fractal interpolation and box dimension},
  author={Michael F. Barnsley and Peter Massopust},
  journal={Journal of Approximation Theory},
  year={2012},
  volume={192},
  pages={362-378}
}
In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarevi\'{c} 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.