SCALING EXPONENTS FOR ELECTRICAL RESISTANCE ON HIGHER-DIMENSIONAL GENERALIZATIONS OF FRACTAL CARPETS AND SPONGES

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

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-5

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.

Keywords: Fractals; Sierpinski Carpet; Menger Sponge; Power-Law Scaling; Electrical Resistance; Potential Theory; Dielectric Theory; Perforated Fractal (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500457

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