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An interface problem for a Sierpinski and a Vicsek fractal

✍ Scribed by Volker Metz; Peter Grabner

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
236 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We suggest a flexible way to study the self‐similar interface of two different fractals. In contrast to previous methods the participating energies are modified in the neighborhood of the intersection of the fractals. In the example of the Vicsek snowflake and the 3‐gasket, a variant of the Sierpinski gasket, we calculate the admissible transition constants via the “Short‐cut Test”. The resulting range of values is reinterpreted in terms of traces of Lipschitz spaces on the intersection. This allows us to describe the interface effects of different transition constants and indicates the techniques necessary to generalize the present interface results. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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