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On the affine self-similarities of the three-dimensional Penrose pattern

Nicolae Cotfas

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We prove that the vertex set of the usual three-dimensional Penrose tiling admits an infinite number of independent scaling factors and an infinite number of inflation centres. More exactly, we prove that there exist an infinite number of real numbers and an infinite number of points such that .


PACS

05.45.Df Fractals

61.44.Br Quasicrystals

MSC

60G18 Self-similar processes

52C23 Quasicrystals, aperiodic tilings

Subjects

Condensed matter: structural, mechanical & thermal

Statistical physics and nonlinear systems

Dates

Issue 35 (4 September 1998)

Received 16 April 1998



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