A. A. Polyakov
АННОТАЦИЯ
As it have been shown earlier, fractals of five-pointed stars allow to repeat the structure of the Penrose tiling, which is the initial model for the crystal lattice of decagonal quasicrystals. Deflationary and inflationary approaches to the construction the fractals of five-pointed stars are offered. In the deflationary approach, at each stage, the regular five-pointed stars of the same orientation and size are placed so, that their centers coincide with the vertices of the polygons of the previous step. The previous prefractal is deleted. In the inflationary approach, the prefractal of the previous step is replicated and placed so, that its centers are coincided with the vertices of increasing regular five-pointed star. The deflationary approach leads to the fragmentation of the structure, the inflationary approach allows joining the stars into increasing clusters. It is shown, how deflationary and inflationary approaches are related. The absolute and relative descriptions of the fractals of five-pointed stars are also considered. In the absolute description, the absolute size and orientation of the building elements are recorded. In the relative description, there are used the changes of these characteristics at each stage of the fractal construction.
КЛЮЧЕВЫЕ СЛОВА:
fractals, Penrose tiling, quasiperiodic lattice, quasicrystals.