Eightfold quasi-periodic
شبه دوري ثمانيEight-pointed stars on an Ammann–Beenker ground: no repeating unit, though every patch of it recurs endlessly.
How it is made
The ground
The pattern is not drawn freehand onto the page. It grows out of this tiling — ammann-beenker — 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 50° and 62°, a range settled by eye.
The numbers
- Ground
- ammann-beenker
- Symmetry
- Quasi-periodic
- Contact angle
- 50°–62°
- Construction
- Hankin polygons-in-contact
Sources
- 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
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