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Representation of discrete sequences with N-dimensional iterated function systems in tensor form

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Abstract

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is self-affine or piecewise self-affine in R 2 or R 3 (R is the set of real numbers). In this paper, the piecewise hidden-variable fractal model is extended from R 3 to R n (n is an integer greater than 3), which is called the multi-dimensional piecewise hidden variable fractal model. This new model uses a “mapping partial derivative” and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the hidden variables. Therefore the result is very general. Moreover, the piecewise hidden-variable fractal model in tensor form is more terse than in the usual matrix form.

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Authors and Affiliations

  1. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing, 100084, China

    Tong Zhang, Jian Lin Liu & Zhuo Zhuang

  2. Solid Mechanics Research Center, Beijing University of Aero & Astro, Beijing, 100083, China

    Tong Zhang

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  1. Tong Zhang
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  2. Jian Lin Liu
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  3. Zhuo Zhuang
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Correspondence to Tong Zhang.

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Zhang, T., Liu, J.L. & Zhuang, Z. Representation of discrete sequences with N-dimensional iterated function systems in tensor form. Nonlinear Dyn 52, 89–93 (2008). https://doi.org/10.1007/s11071-007-9260-z

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  • DOI: https://doi.org/10.1007/s11071-007-9260-z

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