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.
Barnsley, M. F., & Massopust, P. R. (2015). Bilinear fractal interpolation and box dimension. Journal of Approximation Theory, 192, 362–378. https://doi.org/10.1016/j.jat.2014.10.014