Resistance scaling factor of the pillow and fractalina fractals

Michael J. Ignatowich; Daniel J. Kelleher; Catherine E. Maloney; David J. Miller; Khrystyna Serhiyenko

doi:10.1142/S0218348X15500188

Resistance scaling factor of the pillow and fractalina fractals

Michael J. Ignatowich, Daniel J. Kelleher, Catherine E. Maloney, David J. Miller, Khrystyna Serhiyenko

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Much is known in the analysis of a finitely ramified self-similar fractal when the fractal has a harmonic structure: a Dirichlet form which respects the self-similarity of a fractal. What is still an open question is when such a structure exists in general. In this paper, we introduce two fractals, the fractalina and the pillow, and compute their resistance scaling factor. This is the factor which dictates how the Dirichlet form scales with the self-similarity of the fractal. By knowing this factor one can compute the harmonic structure on the fractal. The fractalina has scaling factor (3+41)/16, and the pillow fractal has scaling factor 1/[3]{2}.

Original language	English
Article number	1550018
Journal	Fractals
Volume	23
Issue number	2
DOIs	https://doi.org/10.1142/S0218348X15500188
State	Published - Jun 1 2015

Bibliographical note

Publisher Copyright:
© 2015 World Scientific Publishing Company.

Funding

Research supported in part by NSF Grant DMS 0505622. The authors would like to thank Alexander Teplyaev for his insight and guidance.

Funders	Funder number
National Science Foundation (NSF)	1106982, DMS 0505622

Keywords

Analysis on Fractals
Dirichlet Forms
Electric Networks
Resistance Forms
Self-Similar Fractals

ASJC Scopus subject areas

Modeling and Simulation
Geometry and Topology
Applied Mathematics

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10.1142/S0218348X15500188

Cite this

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AU - Serhiyenko, Khrystyna

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Resistance scaling factor of the pillow and fractalina fractals

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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