The Open Cybernetics & Systemics Journal

2014, 8 : 869-872
Published online 2014 December 31. DOI: 10.2174/1874110X01408010869
Publisher ID: TOCSJ-8-869

Patterns with Symmetries of the Wallpaper Group on the Hyperbolic Space

Peichang Ouyang , Zhanglin Li and Tao Yu
Computer Faculty, China University of Geosciences, China.

ABSTRACT

Equivariant function with respect to symmetries of the wallpaper group is constructed by trigonometric functions. A proper transformation is established between Euclidean plane and hyperbolic spaces. With the resulting function and transformation, wallpaper patterns on the Poincaré and Klein models are generated by means of dynamic systems. This method can be utilized to produce infinity of beautiful pattern automatically.

Keywords:

Hyperbolic geometry, klein model, poincaré model, wallpaper groups.