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Proceedings Paper

Fractal transformations of harmonic functions
Author(s): Michael F. Barnsley; Uta Freiberg
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Paper 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.

Paper Details

Date Published: 3 January 2007
PDF: 12 pages
Proc. SPIE 6417, Complexity and Nonlinear Dynamics, 64170C (3 January 2007); doi: 10.1117/12.696052
Show Author Affiliations
Michael F. Barnsley, The Australian National Univ. (Australia)
Uta Freiberg, The Australian National Univ. (Australia)

Published in SPIE Proceedings Vol. 6417:
Complexity and Nonlinear Dynamics
Axel Bender, Editor(s)

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