The art of tiling originated very early in the history of civilization. Almost every known human society has made use of tilings in some form or another. In particular, tilings using only regular polygons have great visual appeal. Decorated regular tilings with continuous and symmetrical patterns were widely used in decoration field, such as mosaics,… (More)
A fractal tiling (f-tiling) is a tiling whose boundary is fractal. This article presents two families of rare, infinitely many f-tilings. Each f-tiling is constructed by reducing tiles by a fixed scaling factor, using a single prototile, which is a segment of a regular polygon. The authors designed invariant mappings to automatically produce appealing… (More)
This third installment of the Beautiful Math articles considers the visualization of aesthetic patterns with hyperbolic-triangle-group symmetries. A flexible form of invariant mappings contributes to a simple, efficient way to generate hyperbolic patterns. Combined with conformal mappings, this method can yield an abundance of exotic patterns.
A simple, fast method generates various visually appealing spiral patterns. The method is based on the concept that spiral patterns comprise a symmetry group of tilings. It employs invariant mappings and a dynamical system to create seamless colored patterns.