The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group

Abstract EN

By constructing invariant mappings associated with wallpaper groups, this paper presents a simple and efficient method to generate colorful wallpaper patterns.

Although the constructed mappings have simple form and only two parameters, combined with the color scheme of orbit trap algorithm, such mappings can create a great variety of aesthetic wallpaper patterns.

The resulting wallpaper patterns are further projected by central projection onto the sphere.

This creates the interesting spherical patterns that possess infinite symmetries in a finite space.