No Access

MULTI-DIMENSIONAL SELF-AFFINE FRACTAL INTERPOLATION MODEL

TONG ZHANG

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

Corresponding author.

Search for more papers by this author

and

ZHUO ZHUANG

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

Search for more papers by this author

https://doi.org/10.1142/S0219525906000641Cited by:0 (Source: Crossref)

Abstract

Iterated function system (IFS) models have been explored to represent discrete sequences where the attractor of an IFS is self-affine either in R² or R³ (R is the set of real numbers). In this paper, the self-affine IFS model is extended from R³ to Rⁿ (n is 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:

References

A. Carpinteri, L. Dimastrogiovanni and N. Pugno, Int. J. Fracture 131(2), 131 (2005). Crossref, Web of Science, Google Scholar
A. Carpinteri and N. Pugno, Magazine Concrete Res. 57(6), 309 (2005). Crossref, Web of Science, Google Scholar
A. Carpinteri, B. Chiaia and P. Cornetti, Comput. Structures 82(6), 499 (2004). Crossref, Web of Science, Google Scholar
H.-T. Chu and C.-C. Chen, Comput. Graph. 27, 407 (2003). Crossref, Web of Science, Google Scholar
D. S. Mazel and H. H. Manson, IEEE Trans. Signal Processing 40(7), 1724 (1992). Crossref, Web of Science, Google Scholar
D. S. Mazel, IEEE Trans. Signal Processing 42(11), 3269 (1994). Crossref, Web of Science, Google Scholar
D. S. Mazel and H. H. Manson, Hidden-variable fractal interpolation of discrete sequence, Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing5 (1991) pp. 3393–3396. Google Scholar
M. Peruggia, Discrete Iterated Function Systems (Wellesley, Massachusetts, 1993) pp. 12–31. Crossref, Google Scholar
O. I. Craciunescuet al., IEEE Trans. Biomed. Eng. 48(4), 462 (2001). Crossref, Web of Science, Google Scholar
O. I. Craciunescuet al., Bioeng. Division, ASME 54, 207 (2002). Web of Science, Google Scholar
O. I. Craciunescu, S. K. Das and T. V. Samulski, Piecewise fractal interpolation models to reconstruct the three-dimensional tumor perfusion, Proc. Annual Int. Conf. of the IEEE Engineering in Medicine and Biology1 (2000) pp. 292–305. Google Scholar
M. Barnsley, SIAM J. Math. Anal. 20(5), 1218 (1989). Crossref, Web of Science, Google Scholar
M. F. Barnsley, Fractals Everywhere (Academic Press Professional, Boston, 1993) p. 236. Google Scholar
W. C. Strahle, AIAA J. 29(3), 409 (1991). Crossref, Google Scholar
M. A. Marvasti and W. C. Strahle, Signal Processing 41, 191 (1995). Crossref, Web of Science, Google Scholar
M. F. Barnsley, Constructive Approximation 2, 303 (1986). Crossref, Web of Science, Google Scholar
M. F. Barnsley, J. H. Elton and D. P. Hardin, Constructive Approximation 5, 3 (1989). Crossref, Web of Science, Google Scholar