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Scaling Exponents For Electrical Resistance On Higher-Dimensional Generalizations Of Fractal Carpets And Sponges

Author

Listed:
  • JONATHAN F. SCHONFELD

    (Center for Astrophysics, Harvard and Smithsonian, 60 Garden St., Cambridge, Massachusetts 02138, USA)

Abstract

In this paper, we calculate electrical resistance scaling exponents for analogues of “carpet†and “sponge†fractals in higher-dimensional embedding spaces. The calculation idealizes the voids that define such fractals as spherical, and exploits the elementary theory of dielectrics. Possible applications include models of elementary particles with “extra†dimensions, and new large-dimension methods for the theory of fractals.

Suggested Citation

  • Jonathan F. Schonfeld, 2023. "Scaling Exponents For Electrical Resistance On Higher-Dimensional Generalizations Of Fractal Carpets And Sponges," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-5.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:05:n:s0218348x23500457
    DOI: 10.1142/S0218348X23500457
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