Construction of Fractals based on Catalan Solids
Construction of Fractals based on Catalan Solids
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基于加泰罗尼亚多面体的分形构造
DOI：
10.5815/ijmsc.2017.04.01
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Katunin
中科院分区：
文献类型：
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作者：
A. Katunin
确定性分形在计算机图形学和数学科学中起着重要的作用。了解这种分形的构造，特别是从各种类型的多面体构造分形的能力，对于与纯数学问题以及理论物理的一些问题相关的一些问题至关重要。本文提出并讨论了基于Catalan体构造分形的可能性。提出了构造多面体严格确定性分形的方法和算法。它表明，只能从有限数量的加泰罗尼亚固体由于这些固体的特定几何性质的分形构造。给出了基于Catalan体构造的相邻收缩分形的收缩比和分形维数。
The deterministic fractals play an important role in computer graphics and mathematical sciences. The understanding of construction of such fractals, especially an ability of fractals construction from various types of polytopes is of crucial importance in several problems related both to the pure mathematical issues as well as some issues of theoretical physics. In the present paper the possibility of construction of fractals based on the Catalan solids is presented and discussed. The method and algorithm of construction of polyhedral strictly deterministic fractals is presented. It is shown that the fractals can be constructed only from a limited number of the Catalan solids due to the specific geometric properties of these solids. The contraction ratios and fractal dimensions are presented for existing fractals with adjacent contractions constructed based on the Catalan solids.