Разгадка тайны гравюры М. К. Эшера "Всадники"

Abstract

The easiest way to build an ornament that completely fills the plane is to fill it with rapport, that is, with a repetitive part of the ornament, in which the pattern adjacent to one side is a continuation of the pattern adjacent to the opposite side. Usually, a rapport is a rectangle, a rhombus, a regular triangle, or a regular hexagon containing a pattern drawn according to certain rules. In addition, there are countless parquets made up of regular and irregular polygons. These include regular and semi-correct parquet. Semi-correct parquets are divided into homogeneous and heterogeneous parquets. In turn, non-uniform parquets are divided into periodic and non-periodic parquets and so on. Unfortunately, at present, methods of constructing figures that stylize images of animals and plants and fill the plane completely are not the subject of scientific research. After M.K. Escher, no one else worked on figured tiles in the form of animals and plants. A rule to creating a figured tile that fills a plane without overlaps and gaps with translations and reflection symmetries of its repetitions, in particular, the figured tile in the form of an animal or a plant is proposed. The creating the figured tile combining the images of a man and a horse on the M. C. Escher’s print ‘Horsemen’ is considered. The proposed rule was applied to composition ornaments, stylizing M. C. Escher’s prints ‘Horsemen’, ‘Swans’, ‘Fish and Scales’, and ‘Day and Night’. It is assumed that the subject of further research will be to devote the mystery of the engraving by M.K. Escher “Reptiles”.