Constructing of Penrose tiling by means of the fractal of five-pointed stars
- Authors: Polyakov A.A.1
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Affiliations:
- South-Ural State University
- Issue: Vol 2016, No 2 (2016)
- Pages: 121-123
- Section: Article
- URL: https://journals.rcsi.science/0036-0295/article/view/170344
- DOI: https://doi.org/10.1134/S0036029516020129
- ID: 170344
Cite item
Abstract
Fractal i0w(1b) (in author’s notation) of five-pointed stars is considered. The initiator of the fractal is a five-pointed star. When building the fractal, the prefractals of previous step are situated so as their centers coincide with the vertices of a five-pointed star. This star is called a “generalized star.” The size of the generalized star increases τ times at each step, where τ ≈ 1.618 is the golden mean. The orientation of the generalized star reverses at each step. A comparison of the internal parts of the fractal with the layers of the Wieringa roof (layers of Penrose tiling) shows their similarity. Computer simulation confirms that the two-dimensional Penrose tiling can be constructed from a set of four types of fractal i0w(1b).
About the authors
A. A. Polyakov
South-Ural State University
Author for correspondence.
Email: pol_959@mail.ru
Russian Federation, pr. Lenina 76, Chelyabinsk, 454080