  We consider a construction of recurrent fractal interpolation surfaces with
function vertical scaling factors and estimation of their box-counting
dimension. A recurrent fractal interpolation surface (RFIS) is an attractor of
a recurrent iterated function system (RIFS) which is a graph of bivariate
interpolation function. For any given data set on rectangular grids, we
construct general recurrent iterated function systems with function vertical
scaling factors and prove the existence of bivariate functions whose graph are
attractors of the above constructed RIFSs. Finally, we estimate lower and upper
bounds for the box-counting dimension of the constructed RFISs.
