C&SA | Contents

Volume 55 >>> № 2 MARCH — APRIL 2019

UDC 510+004.94

V.I. Shynkarenko¹

¹ Dnipropetrovsk National University of Railway Transport named after academician V. Lazaryan, Dnipro, Ukraine

CONSTRUCTIVE-SYNTHESIZING REPRESENTATION OF GEOMETRIC FRACTALS

Abstract. A constructive-production approach to the generation of fractals is proposed, which is more general than other known approaches. The possibilities of application are shown: great variability of the attributes and initial elements of the formation of fractals; combination of fractals in multifractals. The possibilities of fractal generation are extended by eliminating the constraints necessary for other approaches. The proposed approach allowed us to establish several properties of fractional dimension that were previously unknown, which allow its change in the process of fractal generation and mismatch of fractional dimensions of the form limit in the process of generation and the limiting fractal. A simple definition of a deterministic geometric fractal that takes into account all the characteristic properties is given.

Keywords: constructor, fractal, multifractal, fractional dimension, Sierpinski triangle, fractal geometry.

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