MULTI-DIMENSIONAL SELF-AFFINE FRACTAL INTERPOLATION MODEL

Tong Zhang () and Zhuo Zhuang
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Tong Zhang: Department of Engineering Mechanics, School of Aerospace,Tsinghua University, Beijing, 100084, China
Zhuo Zhuang: Department of Engineering Mechanics, School of Aerospace,Tsinghua University, Beijing, 100084, China

Advances in Complex Systems (ACS), 2006, vol. 09, issue 01n02, 133-146

Abstract: Iterated function system (IFS) models have been explored to represent discrete sequences where the attractor of an IFS is self-affine either inR2orR3(Ris the set of real numbers). In this paper, the self-affine IFS model is extended fromR3toRn(nis an integer and greater than 3), which is called the multi-dimensional self-affine fractal interpolation model. This new model is presented by introducing the defined parameter "mapping partial derivative." A constrained inverse algorithm is given for the identification of the model parameters. The values of new model depend continuously on all of the variables. That is, the function is determined by the coefficients of the possibly multi-dimensional affine maps. So the new model is presented as much more general and significant.

Keywords: Iterated function system; self-affine; fractal interpolation model (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0219525906000641

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