Cybernetics and Systems Analysis

, Volume 55, Issue 2, pp 186–199 | Cite as

Constructive-Synthesizing Representation of Geometric Fractals

  • V. I. ShynkarenkoEmail author


A constructive-production approach, which is more general than other well-known approaches, is proposed to generate fractals. Possibilities are shown for using a large variability of attributes and initial elements of formation of fractals, as well as combining fractals into multifractals. The possibilities of generating fractals are extended by eliminating the constraints necessary in other approaches. The proposed approach allowed to establish several previously unknown properties of fractional dimension that consist of the possibility of changing it in the process of generation of a fractal and a mismatch of fractional dimensions of the form limit during generation and the limiting fractal. A simple definition of a deterministic geometric fractal is given. This definition takes into account all the properties characterizing such a fractal.


constructor fractal multifractal fractional dimension Sierpinski triangle fractal geometry 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.V. Lazaryan Dnipropetrovsk National University of Railway TransportDniproUkraine

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