Weaving patterns inspired by the pentagon snub subdivision scheme. Issue 1 (3rd April 2022)

• Record Type: Journal Article
• Authors: Lipschütz, Henriette; Reitebuch, Ulrich; Skrodzki, Martin; Polthier, Konrad
• Is Part Of: Journal of mathematics and the arts. Volume 16:Issue 1/2(2022)
• Page Start: 75
• Page End: 103
• Publication Date: 2022-04-03
• Subjects: Mesh subdivision schemes -- pentagons -- fractals -- weaving -- paper models -- jigsaw puzzles -- visual and tactile illustration; Arts -- Mathematics -- Periodicals; 700.151
• DOI: 10.1080/17513472.2022.2069417
• Languages: English
• ISSNs: 1751-3472

Abstract

Abstract : Various computer simulations regarding, e.g. the weather or structural mechanics, solve complex problems on a two-dimensional domain. They mostly do so by splitting the input domain into a finite set of smaller and simpler elements on which the simulation can be run fast and efficiently. This process of splitting can be automatized by using subdivision schemes. Given the wide range of simulation problems to be tackled, an equally wide range of subdivision schemes is available. This paper illustrates a subdivision scheme that splits the input domain into pentagons. Repeated application gives rise to fractal-like structures. Furthermore, the resulting subdivided domain admits to certain weaving patterns. These patterns are subsequently generalized to several other subdivision schemes. As a final contribution, we provide paper models illustrating the weaving patterns induced by the pentagonal subdivision scheme. Furthermore, we present a jigsaw puzzle illustrating both the subdivision process and the induced weaving pattern. These transform the visual and abstract mathematical algorithms into tactile objects that offer exploration possibilities aside from the visual. GRAPHICAL ABSTRACT: UF0001