Representation of discrete sequences with high-dimensional iterated function systems |
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Authors: | Tong Zhang Zhuo Zhuang |
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Affiliation: | (1) Solid Mechanics Research Center, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China;(2) Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing, 100084, China |
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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 piece-wise self-affine in R 2 or R 3 (R is the set of real numbers). In this paper, the piece-wise hidden-variable fractal model is extended from R 3 to R n (n is an integer greater than 3), which is called the high-dimensional piece-wise 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. |
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Keywords: | Discrete sequences Fractal interpolation Iterated Function System Piece-wise hidden-variable fractal model |
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