Smoothness of Coalescence Hidden-Variable Fractal Interpolation Surfaces

In the present paper, the stability of Coalescence Hidden variable Fractal Interpolation Sur- faces(CHFIS) is established. The estimates on error in approximation of the data generating function by CHFIS are found when there is a perturbation in independent, dependent and hidden variables. It is proved that any small perturbation in any of the variables of generalized interpolation data results in only small per- turbation of CHFIS. Our results are likely to be useful in investigations of texture of surfaces arising from the simulation of surfaces of rocks, sea surfaces, clouds and similar natural objects wherein the generating function depends on more than one variable.

[1]  SCALING BEHAVIOUR OF A MULTIPLY CONNECTED FLUCTUATING INTERFACE IN TWO DIMENSIONS , 2003 .

[2]  Stability of affine coalescence hidden variable fractal interpolation functions , 2008 .

[3]  Leoni Dalla,et al.  BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON GRIDS , 2002 .

[4]  Claude Tricot,et al.  Fractals in Engineering , 1997 .

[5]  C. Lung,et al.  Fractal dimension of the fractured surface of materials , 1989 .

[6]  Heping Xie,et al.  The Study on Bivariate Fractal Interpolation Functions and Creation of Fractal Interpolated Surfaces , 1997 .

[7]  Hassan Zahouani,et al.  Fractal models of surface topography and contact mechanics , 1998 .

[8]  Michael F. Barnsley,et al.  The calculus of fractal interpolation functions , 1989 .

[9]  A. Provenzale,et al.  A search for chaotic behavior in large and mesoscale motions in the Pacific Ocean , 1986 .

[10]  K. Birdi.  Fractals in Chemistry, Geochemistry, and Biophysics , 1993, Springer US.

[11]  A. K. B. Chand,et al.  Hidden Variable Bivariate Fractal Interpolation Surfaces , 2003 .

[12]  John A. Belward,et al.  Fractal dimensions for rainfall time series , 1999 .

[13]  Michael F. Barnsley,et al.  Fractal functions and interpolation , 1986 .

[14]  Douglas P. Hardin,et al.  Fractal Interpolation Surfaces and a Related 2-D Multiresolution Analysis , 1993 .

[15]  A. Chand,et al.  Smoothness Analysis of Coalescence Hidden Variable Fractal Interpolation Functions , 2007 .

[16]  Robert Malysz,et al.  The Minkowski dimension of the bivariate fractal interpolation surfaces , 2006 .

[17]  Tom Zimmermann,et al.  The fractal appearance of interstellar clouds , 1992 .

[18]  B. Mandelbrot.  Fractal Geometry of Nature , 1984 .

[19]  P. Massopust.  Fractal Functions, Fractal Surfaces, and Wavelets , 1995 .

[20]  B. Mandelbrot.  Stochastic models for the Earth's relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. , 1975, Proceedings of the National Academy of Sciences of the United States of America.