Tenfold quasi-periodic
شبه دوري عشاريTen-pointed stars in a field that never repeats: decagonal quasi-periodic order of the kind Lu and Steinhardt identified at the Darb-i Imam shrine, Isfahan (1453).
How it is made
The ground
The pattern is not drawn freehand onto the page. It grows out of this tiling — penrose — which never appears in the finished drawing and decides everything in it.
The contact angle
At the middle of every edge sits a point. Two rays leave it into the tile, each at the same angle from that edge, and run until they meet another. That angle is the whole parameter. This family is drawn between 45° and 52°, a range settled by eye.
The numbers
- Ground
- penrose
- Symmetry
- Quasi-periodic
- Contact angle
- 45°–52°
- Construction
- Hankin polygons-in-contact
Sources
- Lu, Peter J. and Steinhardt, Paul J. (2007). Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture. Science. 315, 1106–1110. read it10.1126/science.1135491
- de Bruijn, N. G. (1981). Algebraic theory of Penrose's non-periodic tilings of the plane, I and II. Indagationes Mathematicae (Proc. Kon. Nederl. Akad. Wetensch. Ser. A 84). 43, 39–52 and 53–66.
- Kaplan, Craig S. (2005). Islamic Star Patterns from Polygons in Contact. Proceedings of Graphics Interface 2005. pp. 177–185. read it
Type any name and it picks one of these fifteen, and an angle inside that family's band. The number the letters carry is what chooses.
Make one from a name →