Construction of Recurrent Fractal Interpolation Surfaces with Function Scaling Factors and Estimation of Box-counting Dimension on Rectangular Grids

摘要

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