Randomness and Topological Invariants in Pentagonal Tiling Spaces
Author
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-23, 23 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-06-30
Country of Publication
Egypt
No. of Pages
23
Main Subjects
Abstract EN
We analyze substitution tiling spaces with fivefold symmetry.
In the substitution process, the introduction of randomness can be done by means of two methods which may be combined: composition of inflation rules for a given prototile set and tile rearrangements.
The configurational entropy of the random substitution process is computed in the case of prototile subdivision followed by tile rearrangement.
When aperiodic tilings are studied from the point of view of dynamical systems, rather than treating a single one, a collection of them is considered.
Tiling spaces are defined for deterministic substitutions, which can be seen as the set of tilings that locally look like translates of a given tiling.
Čech cohomology groups are the simplest topological invariants of such spaces.
The cohomologies of two deterministic pentagonal tiling spaces are studied.
American Psychological Association (APA)
Escudero, Juan García. 2011. Randomness and Topological Invariants in Pentagonal Tiling Spaces. Discrete Dynamics in Nature and Society،Vol. 2011, no. 2011, pp.1-23.
https://search.emarefa.net/detail/BIM-510424
Modern Language Association (MLA)
Escudero, Juan García. Randomness and Topological Invariants in Pentagonal Tiling Spaces. Discrete Dynamics in Nature and Society No. 2011 (2011), pp.1-23.
https://search.emarefa.net/detail/BIM-510424
American Medical Association (AMA)
Escudero, Juan García. Randomness and Topological Invariants in Pentagonal Tiling Spaces. Discrete Dynamics in Nature and Society. 2011. Vol. 2011, no. 2011, pp.1-23.
https://search.emarefa.net/detail/BIM-510424
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-510424