Results are presented on the existence, coding theory, functional equations and moment theory for such fractal interpolation functions. Applications to the approximation of naturally wiggly functions, which may show some kind of geometrical self-similarity under magnification, such as profiles of cloud tops and mountain ranges, are envisaged.doi:10.1007/BF01893434Michael...
M.F. Barnsley Fractal functions and interpolation Constructive Approximation (1986) M.F. Barnsley J.S. Bendat et al. J. Feder B.B. Mandelbrot There are more references available in the full text version of this article. Cited by (51) A hybrid method for noise suppression using variational...
Xie H,Sun H.The Study on Bivariate Fractal Interpolation Functions and Creation of Fra- ctal Interpolation Surface[J].Fractals,1997, 5(4):625-634.Xie H, Sun H. The Study on Bivariate Fractal Interpolation Functions and Creation of Fractal Interpolation Surface[J].Fractals, 1997,5(4) :625-...
In this paper, the methods of construction of a fractalsurface are introduced, the principle of bivariate fractalinterpolation functions is discussed. The theorem of the uniquenessof an iterated function system of bivariate fractal interpolationfunctions is proved. Moreover, the theorem of fractal dimens...
Graphical representations of fractal calculus of fractal interpolation functions and Weierstrass functions are presented. Keywords: fractal calculus; fractal dimensions; weierstrass function; fractal interpolation function MSC: 28A80; 94A17; 60E07; 82Cxx...
Offers a comprehensive presentation of fractal functions and fractal surfaces Includes latest developments in fractal interpolation Connects fractal geometry with wavelet theory Includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, and further develops...
Barnsley, M.F.: Fractal functions and interpolation. Constr. Approx. 2, 303–329 (1986) Article MathSciNet Google Scholar Barnsley, M.F.: Fractal image compression. Not. Am. Math. Soc. 43, 657–662 (1996) MathSciNet Google Scholar Barnsley, M.F.: Theory and applications of fractal...
Fractal interpolation functionsiterated function systemsSchauder basesThe objective of the present paper is the study of affine transformations of the plane, which provide self-affine curves as attractors. The properties of these curves depend decisively of the coefficients of the system of affnities ...
[1] P. Bouboulis and L. Dalla, “Closed fractal interpolation surfaces,” Journal of Mathematical Analysis and Applications, vol. 327, no. 1, pp. 116–126, 2007. [2] M. F. Barnsley, “Fractal functions and interpolation,” Constructive Approximation, vol. 2, no. 4, pp. 303–329, ...
In the present paper, we introduce a construction of hidden variable fractal interpolation functions (HVFIFs) in R2 by IFSs with four function contractivity factors and analyze their smoothness and stability, which are similar to ones in [21,22]. We obtain the lower and upper bounds for box...