Homeotoxal and Homeohedral Tiling Using Pasting Scheme

S. Jebasingh,a,* Robinson Thamburajb and Atulya K. Nagarc

Homeotoxal and Homeohedral Tiling Using Pasting Scheme

Authors :

S. Jebasingh,a,* Robinson Thamburaj^b and Atulya K. Nagar^c

Author Address :

^aDepartment of Mathematics, Karunya University, Coimbatore, India.
^bDepartment of Mathematics, Madras Christian College, Tambaram, Chennai - 600 059, India.
^cDepartment of Mathematics and Computer Science, Liverpool Hope University, Hope Park, Liverpool, L16 9JD, United Kingdom.

*Corresponding author.

Abstract :

The art of tiling has been in practice from the beginning of human civilization. Intricate tiling patterns were used to decorate and cover floors and walls [1]. Robinson Thamburaj introduced the notion of pasting rules [4] and studied the construction of kolam tiling. In this paper we study Pasting Scheme (PS) using special sets of tiles namelyWang tile, Escher tile and Truchet tile. The scheme is also used to construct the five types of Homeotoxal tiling [1] and the eleven types of Homeohedral tiling [1]. Generalizing Pasting Scheme we define Tabled Pasting Scheme (TPS) where pasting rules are grouped in tables and the tables of rules are used as many times as given in the scheme for the successive construction of a tiling.