Construction and box dimension of recurrent fractal interpolation surfaces
Zhen Liang
Nanjing Audit University, ChinaHuo-Jun Ruan
Zhejiang University, Hangzhou, China
Abstract
In this paper, we present a general framework to construct recurrent fractal interpolation surfaces (RFISs) on rectangular grids. Then we introduce bilinear RFISs, which are easy to be generated while there are no restrictions on interpolation points and vertical scaling factors. We also obtain the box dimension of bilinear RFISs under certain constraints, where the main assumption is that vertical scaling factors have uniform sums under a compatible partition.
Cite this article
Zhen Liang, Huo-Jun Ruan, Construction and box dimension of recurrent fractal interpolation surfaces. J. Fractal Geom. 8 (2021), no. 3, pp. 261–288
DOI 10.4171/JFG/105