Penrose tiling fractality in coordination Cayley’s tree graphs representation

A.N. Mihalyuk, P.L. Titov and V.V. Yudin

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 19, 4127-4139

Abstract: We offer the mathematical apparatus for mapping lattice and cellular systems into the generalized coordination Cayley’s tree graphs. These Cayley’s trees have a random branchiness property and an intralayer interbush local intersection. Classical Bethe-Cayley tree graphs don’t have these properties. Bush type simplicial decomposition on Cayley’s tree graphs is introduced, on which the enumerating polynomials or enumerating distributions are built. Within the entropy methodology three types of fractal characteristics are introduced, which characterize quasi-crystalline pentagonal Penrose tiling. The quantitative estimate for the frontal-radial fractal percolation on a Cayley’s tree graph of a Penrose tiling leading to the overdimensioned effect is calculated.

Keywords: Penrose tiling; Coordination Cayley’s tree graphs; Percolation; Fractality (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:19:p:4127-4139

DOI: 10.1016/j.physa.2010.06.008

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