  Starting from the classical results of Shubnikov and Zamorzayev, computer
models of shapes are implemented, which allow to visualize the action of
discrete subgroups of continuous topological groups. The action is visualize by
performing partitions of the shapes into the fundamental domains of the
discrete symmetry groups of similarity, the definition of which was given by
Zamorzaev. Particular attention is paid to the models of quasilattice, with the
help of which such tiling of figures are constructed, that their multicolored
coloring allows us to investigate, including the action of colored groups of
symmetry of similarity. It is shown that for two-dimensional quasicrystals
(quasi-lattices) the homothety coefficients are integers algebraic numbers of
the quadratic expansion of the field of rational numbers. Some conformal
mappings of crystal sets have been studied, which made it possible to establish
the correspondence between the stereocyclic projection and the coordinate
system of inverse radii.
