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Asymptotics for the spectral and walk dimension as fractals approach Euclidean space

Abstract:

We discuss the behavior of the dynamic dimension exponents for families of fractals based on the Sierpinski gasket and carpet. As the length scale factor for the family tends to infinity, the lattice approximations to the fractals look more like the tetrahedral or cubic lattice in Euclidean space and the fractal dimension converges to that of the embedding space. However, in the Sierpinski gasket case, the spectral dimension converges to two for all dimensions. In two dimensions, we prove a c...

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Publication status:
Published

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Publisher copy:
10.1142/S0218348X02001270

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
Volume:
10
Issue:
4
Pages:
403-412
Publication date:
2002-12-05
DOI:
EISSN:
1793-6543
ISSN:
0218-348X
URN:
uuid:c1eb6b6c-91ef-4930-87c8-d31c00a0c6cf
Source identifiers:
4133
Local pid:
pubs:4133

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