Construction of Fractals of Stars: Inflationary and Deflationary Approaches

Abstract

Inflationary and deflationary approaches to constructing fractals from regular five-pointed stars are considered. Two types of description of these approaches, namely, absolute and relative, are proposed. The relative description makes it possible to formulate a simple relation between these approaches. The deflationary approach is as follows: at each stage of constructing a fractal, regular five-pointed stars of the same size and orientation are arranged so that their centers coincide with the vertices of the polygons of the previous step. The star sizes at each step can be reduced in proportion to an integer degree of the golden section. The inflationary approach is as follows: the prefractal of the previous step multiplies, and the resulting figures are arranged so that their centers coincide with the vertices of a regular five-pointed star, which grows in size.