MULTI-DIMENSIONAL PIECE-WISE SELF-AFFINE FRACTAL INTERPOLATION MODEL IN TENSOR FORM

Tong Zhang (), Jianlin Liu and Zhuo Zhuang
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Tong Zhang: Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing, 100084, China
Jianlin Liu: 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 03, 287-293

Abstract: Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine inR2orR3(Ris the set of real numbers). In this paper, the piece-wise self-affine IFS model is extended fromR3toRn(nis an integer greater than 3), which is called the multi-dimensional piece-wise self-affine fractal interpolation model.This model uses a "mapping partial derivative" and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the model parameters, and represent most data which are not multi-dimensional self-affine inRn. Therefore, the result is very general. Moreover, the multi-dimensional piece-wise self-affine fractal interpolation model in tensor form is more terse than in the usual matrix form.

Keywords: Piece-wise self-affine; iterated function system; fractal interpolation (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0219525906000756

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