3 January 2007 Fractal transformations of harmonic functions
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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.
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Michael F. Barnsley, Michael F. Barnsley, Uta Freiberg, Uta Freiberg, } "Fractal transformations of harmonic functions", Proc. SPIE 6417, Complexity and Nonlinear Dynamics, 64170C (3 January 2007); doi: 10.1117/12.696052; https://doi.org/10.1117/12.696052
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