Penrose tiling fractality in coordination Cayley’s tree graphs representation

Autor:	A.N. Mihalyuk, P.L. Titov, V.V. Yudin
Rok vydání:	2010
Předmět:	Statistics and Probability Combinatorics Discrete mathematics Vertex-transitive graph Fractal Cayley graph Cayley transform Condensed Matter Physics Tree (graph theory) Simplicial decomposition Mathematics Penrose tiling
Zdroj:	Physica A: Statistical Mechanics and its Applications. 389:4127-4139
ISSN:	0378-4371
DOI:	10.1016/j.physa.2010.06.008
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::265fbc180c5a2d73a2733c93e3c14f11 https://doi.org/10.1016/j.physa.2010.06.008 Zobrazit plný text záznamu Full Text from ScienceDirect