A. A. Polyakov
ABSTRACT
Inflationary and deflationary approaches to the constructing fractals from regular five-pointed stars are considered. Two types of descriptions of these approaches are proposed: absolute and relative. The relative description allows to formulate a simple connection between these approaches. Deflationary approach: at each stage of building 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 size of these stars at each step can be reduced in proportion to the integer degree of the golden mean; the orientation may coincide or be opposite to the orientation of the stars of the previous step. Inflationary approach: the prefractal of the previous step replicates, and the resulting figures are arranged so that their centers coincide with the vertices of a regular five-pointed star, increasing in size.
KEYWORDS
fractals, quasiperiodic lattice, quasicrystals
DOI: 10.7868/S0235010619010158