Skip to main content
SpringerLink
Log in

Theory and application of Pascal-Sierpinski gasket fractals

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

Some combinatorial parameters of Sierpinski gasket (SG) are presented. The more general Pascal-Sierpinski gaskets (PSG) provide a convenient vehicle for the study of resistance in fractal lattices. The combination of the wye-delta (Y-Δ) transformations and selected multiple tracer edges provide a powerful new tool. Connections are made to modeling transport networks: diffusion processes with barriers, random walks, and relaxation phenomena.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. D. Bedrosian and X. Sun, Pascal-Sierpinski Gasket Fractal Networks: Some Resistance Properties,J. Franklin Inst.,326 (4), 503–509 (1989).

    Google Scholar 

  2. W. Sierpinski, Sur une courbe contourienne qui contient une image biunivoque et continue de toute courbe donnee, C.R.Acad. Sci. Paris,162, 629 (1916).

    Google Scholar 

  3. N. S. Holter, A. Lakhtakia,et al., On a New Class of Planar Fractals: the Pascal-Sierpinski Gaskets,J. Phys. A,19, 1753–1759 (1986).

    Google Scholar 

  4. M. F. Barnsley and S. G. Demko,Chaotic Dynamics and Fractals, Academic Press, Orlando (1986).

    Google Scholar 

  5. R. Rammal, Spectrum of Harmonic Excitation on Fractals,J. Physique,45, 191–206 (1984).

    Google Scholar 

  6. J. A. Riera, Relaxation of Hierarchical Models Defined on Sierpinski Gasket Fractals,J. Phys. A,19, L869-L873 (1986).

    Google Scholar 

  7. M. F. Barnsley and A. D. Sloan, A Better Way to Compress Images,Byte, 215–223, Jan. 1988.

  8. J. R. Banavar, A. B. Harris, and J. Koplik, Resistance of Random Walks,Phys. Rev. Lett.,51, 1115–1118 (1983).

    Google Scholar 

  9. H. Taitelbaum and S. Havlin, Superconductivity Exponent for the Sierpinski Gasket in Two Dimension,J. Phys. A,21, 2265–2271 (1988).

    Google Scholar 

  10. S. Roux and C. D. Mitescu, Hierachy of Current Cumulants on a Sierpinski Gasket,Phys. Rev. B,35, 898–901 (1987).

    Google Scholar 

  11. J. M. Gordon and A. M. Goldman, Fractal Dimensions and Dimensional Crossover in Superconducting Wire Networks,Phys. B,152, 125–128 (1988).

    Google Scholar 

  12. L. Pauling,Nature of the Chemical Bond, Cornell University Press, Ithaca, New York, p. 301 (1939).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moore School of Electrical Engineering, University of Pennsylvania, 19104-6390, Philadelphia, PA, USA

    Samuel D. Bedrosian & Xiaoguang Sun

Authors
  1. Samuel D. Bedrosian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoguang Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported in part by a grant from AT&T Information Systems, University Affiliates Program, through the Center for Communication and Information Science and Policy at the Moore School of Electrical Engineering.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bedrosian, S.D., Sun, X. Theory and application of Pascal-Sierpinski gasket fractals. Circuits Systems and Signal Process 9, 147–159 (1990). https://doi.org/10.1007/BF01236448

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01236448

Keywords

Search

Navigation