@inproceedings{7749c25180e2411d8cf9fb1f3496b1d2,
title = "Fractal transformations of harmonic functions",
abstract = "The theory of fractal homeomorphisms is applied to transform a Sierpinski triangle into what we call a Kigami triangle. The latter is such that the corresponding harmonic functions and the corresponding Laplacian Δ take a relatively simple form. This provides an alternative approach to recent results of Teplyaev. Using a second fractal homeomorphism we prove that the outer boundary of the Kigami triangle possesses a continuous first derivative at every point. This paper shows that IFS theory and the chaos game algorithm provide important tools for analysis on fractals.",
author = "Barnsley, {Michael F.} and Uta Freiberg",
year = "2007",
doi = "10.1117/12.696052",
language = "English",
isbn = "0819465259",
series = "Proceedings of SPIE - The International Society for Optical Engineering",
booktitle = "Complexity and Nonlinear Dynamics",
note = "Complexity and Nonlinear Dynamics ; Conference date: 12-12-2006 Through 13-12-2006",
}