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The Fractal Dimension of Sets Derived from Complex Bases

Published online by Cambridge University Press:  20 November 2018

William J. Gilbert
William J. Gilbert*
Affiliation:
Pure Mathematics Department University of Waterloo Waterloo, Ontario N2L 3GL Canada
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Abstract

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For each positive integer n, the radix representation of the complex numbers in the base —n + i gives rise to a tiling of the plane. Each tile consists of all the complex numbers representable in the base -n + i with a fixed integer part. We show that the fractal dimension of the boundary of each tile is 2 log λn/log(n2 + 1), where λn is the positive root of λ3 - (2n - 1) λ2 - (n - 1) 2λ - (n2 + 1).

Keywords

11K5551M20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 4 , 01 December 1986 , pp. 495 - 500
Copyright
Copyright © Canadian Mathematical Society 1986

References

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