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THE HAUSDORFF DIMENSION OF THE BOUNDARY OF A SELF-SIMILAR TILE

Published online by Cambridge University Press:  01 June 2000

P. DUVALL ,
J. KEESLING  and
A. VINCE
P. DUVALL
Affiliation:
Department of Mathematical Sciences, University of North Carolina, Greensboro, NC 27412-0001, USA; [email protected]
J. KEESLING
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA; [email protected], [email protected]
A. VINCE
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA; [email protected], [email protected]
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Abstract

An effective method is given for computing the Hausdorff dimension of the boundary of a self-similar digit tile T in n-dimensional Euclidean space:

formula here

where 1/c is the contraction factor and λ is the largest eigenvalue of a certain contact matrix first defined by Gröchenig and Haas.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 3 , June 2000 , pp. 748 - 760
Copyright
The London Mathematical Society 2000

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