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Regular version of the site
Campus inMoscow
Student
Title
Supervisor
Faculty
Educational Programme
Alexander Korotin
Local Rules for Self-similar Tilings of the Plane by Polygons
Mathematics
(Bachelor’s programme)
2016
Abstract

The work is devoted to studying some special classes of tilings of the plane such as self-similar tilings and indefinitely composable tilings. These tilings are interesting because locally all their regions of any size have similar properties.

The main goal of this work is to describe all self-similar tilings with Ammann Hexagons and L-tiles.

In Chapter 1 of our degree paper we give the main definitions.

In Chapter 2 we study self-similar tilings with the Ammann Hexagons. For these tilings there are some sets of local rules in literature on how to attach tiles to each other so that they force the desired global self-similar structure emerge. We take two of the rules (so called "arrow rule" and "the rule of ellipses") and prove that they are equivalent.

In Chapter 3 we give the constructive way to describe all self-similar L-tilings of the plane without using local rules. Moreover, we prove that the standart local rules for the self-similar L-tilings of the plane do not exist. In addition, we examine another technique to describe the self-similar L-tilings - tilings by the trilobite and the cross.

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