Resistance scaling and random walk dimensions for finitely ramified Sierpinski carpets

We present a new algorithm to calculate the random walk dimension of finitely ramified Sierpinski carpets. The fractal structure is interpreted as a resistor network for which the resistance scaling exponent is calculated using Mathematica. A fractal form of the Einstein relation, which connects dif...

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Bibliographic Details
Published in:SIGSAM bulletin 2000-09, Vol.34 (3), p.1-8
Main Authors: Schulzky, Christian, Franz, Astrid, Hoffmann, Karl Heinz
Format: Article
Language:English
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Summary:We present a new algorithm to calculate the random walk dimension of finitely ramified Sierpinski carpets. The fractal structure is interpreted as a resistor network for which the resistance scaling exponent is calculated using Mathematica. A fractal form of the Einstein relation, which connects diffusion with conductivity, is used to give a numerical value for the random walk dimension.
ISSN:0163-5824
DOI:10.1145/377604.377608