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Journal of the London Mathematical Society 2000 61(3):748-760; doi:10.1112/S0024610700008711
© 2000 by London Mathematical Society
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© The London Mathematical Society

The Hausdorff Dimension of the Boundary of a Self-Similar Tile

P. Duvall, J. Keesling and A. Vince

Department of Mathematical Sciences, University of North Carolina Greensboro, NC 27412-0001, USA, duvallp{at}uncg.edu
Department of Mathematics, University of Florida Gainesville, FL 32611-8105, USA, jek{at}math.ufl.edu
Department of Mathematics, University of Florida Gainesville, FL 32611-8105, USA, vince{at}math.ufl.edu

Received 12 November 1998. Revision received 1 March 1999.

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

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


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