A construction of fractal surfaces with function scaling factors on a rectangular grid
arXiv:1404.1300
Abstract
A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces constructed. We construct IFS with function vertical scaling factors which are 0 on the boundaries of a rectangular grid using arbitrary data set on a rectangular grid and give a condition for an attractor of the IFS constructed being a surface. Finally, lower and upper bounds of Box-counting dimension of the constructed surface are estimated.
arXiv comment9 pages, 2 figures
References in corpus (3)
- Construction of Fractal Surfaces by Recurrent Fractal Interpolation Curves
- Box-counting dimension of a kind of fractal interpolation surface on rectangular grids
- Construction of Recurrent Fractal Interpolation Surfaces with Function Scaling Factors and Estimation of Box-counting Dimension on Rectangular Grids