Visualization of Escher-like Spiral Patterns in Hyperbolic Space

Symmetry

Chongyang Qiu¹  Xinfei Li²  Jianhua Pang²  Peichang Ouyang² 

[1] Human Sciences Department, Gannan University of Science and Technology, Ganzhou 341000, China;School of Science, Guangxi University of Science and Technology, Liuzhou 545006, China;

关键词: spiral;    tiling;    hyperbolic geometry;    visualization;    Escher;   

DOI  :  10.3390/sym14010134

来源: DOAJ

【 摘 要 】

Spirals, tilings, and hyperbolic geometry are important mathematical topics with outstanding aesthetic elements. Nonetheless, research on their aesthetic visualization is extremely limited. In this paper, we give a simple method for creating Escher-like hyperbolic spiral patterns. To this end, we first present a fast algorithm to construct Euclidean spiral tilings with cyclic symmetry. Then, based on a one-to-one mapping between Euclidean and hyperbolic spaces, we establish two simple approaches for constructing spiral tilings in hyperbolic models. Finally, we use wallpaper templates to render such tilings, which results in the desired Escher-like hyperbolic spiral patterns. The method proposed is able to generate a great variety of visually appealing patterns.

【 授权许可】

Unknown