中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90509-090509.doi: 10.1088/1674-1056/19/9/090509

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A new fractal algorithm to model discrete sequences

Heidi Kuzuma1, James W. Rector2, 翟明岳3   

  1. (1)Department of Civil Engineering, University of California, Berkeley 94530, USA; (2)Lawrence Berkeley Laboratory, Berkeley 94530, USA; (3)School of EE Engineering, North China Electric Power University, Beijing 102206, China
  • 收稿日期:2009-10-22 修回日期:2010-04-20 出版日期:2010-09-15 发布日期:2010-09-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 60972004 and 60402004).

A new fractal algorithm to model discrete sequences

Zhai Ming-Yue(翟明岳)a)†, Heidi Kuzumab), and James W. Rectorb)c)   

  1. a School of EE Engineering, North China Electric Power University, Beijing 102206, China; b Department of Civil Engineering, University of California, Berkeley 94530, USA; c Lawrence Berkeley Laboratory, Berkeley 94530, USA
  • Received:2009-10-22 Revised:2010-04-20 Online:2010-09-15 Published:2010-09-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 60972004 and 60402004).

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摘要： Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affine transform, solving the difficulty in determining the vertical scaling factors, one of the most difficult challenges faced by the fractal interpolation. The proposed method is carried out by interpolating the known attractor and the real discrete sequences from seismic data. The results show that a great accuracy in reconstruction of the known attractor and seismic profile is found, leading to a significant improvement over other fractal interpolation schemes.

Abstract: Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affine transform, solving the difficulty in determining the vertical scaling factors, one of the most difficult challenges faced by the fractal interpolation. The proposed method is carried out by interpolating the known attractor and the real discrete sequences from seismic data. The results show that a great accuracy in reconstruction of the known attractor and seismic profile is found, leading to a significant improvement over other fractal interpolation schemes.

Key words: fractal interpolation, the vertical scaling factors, iterative function system, seismic data

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