TY - JOUR
T1 - Weaving patterns inspired by the pentagon snub subdivision scheme
AU - Lipschütz, Henriette
AU - Reitebuch, Ulrich
AU - Skrodzki, Martin
AU - Polthier, Konrad
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - fractals
KW - jigsaw puzzles
KW - Mesh subdivision schemes
KW - paper models
KW - pentagons
KW - visual and tactile illustration
KW - weaving
UR - http://www.scopus.com/inward/record.url?scp=85130142952&partnerID=8YFLogxK
U2 - 10.1080/17513472.2022.2069417
DO - 10.1080/17513472.2022.2069417
M3 - Article
AN - SCOPUS:85130142952
SN - 1751-3472
VL - 16
SP - 75
EP - 103
JO - Journal of Mathematics and the Arts
JF - Journal of Mathematics and the Arts
IS - 1-2
ER -