Construction of Fractals based on Catalan Solids

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Andrzej Katunina 1,*

1. Institute of Fundamentals of Machinery Design, Silesian University of Technology, 18A Konarskiego Street, 44-100 Gliwice, Poland

* Corresponding author.


Received: 17 Jun. 2017 / Revised: 9 Aug. 2017 / Accepted: 18 Sep. 2017 / Published: 8 Nov. 2017

Index Terms

Deterministic fractals, iterated function system, Catalan solids


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.

Cite This Paper

Andrzej Katunin,"Construction of Fractals based on Catalan Solids", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.3, No.4, pp.1-7, 2017.DOI: 10.5815/ijmsc.2017.04.01


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