## 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 |
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Article number | 1550018 |

Journal | Fractals |

Volume | 23 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2015 |

### Bibliographical note

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

Publisher Copyright:

© 2015 World Scientific Publishing Company.

## 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