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).
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References
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Original Russian Text © A.A. Polyakov, 2016, published in Rasplavy, 2016, No. 2, pp. 118–122.
The article was translated by the author.
Articles presented on 14 Russian conference “Structure and Properties of Metal and Slag Melts” (MIShR-14, September 21‒25, 2015, Yekaterinburg).
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Polyakov, A.A. Constructing of Penrose tiling by means of the fractal of five-pointed stars. Russ. Metall. 2016, 121–123 (2016). https://doi.org/10.1134/S0036029516020129
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DOI: https://doi.org/10.1134/S0036029516020129