Peter Hilgers

Ettlingen, Germany

I am a retired engineer, amateur in mathematics and computer hobbyist. Current computers and sophisticated programs make it possible to create, study and visualise complex structures. For me this is a constant source of challenges and delight, especially in the realm of geometry.

40 x 60 cm
Digital print, created with Mathematica and Blender

The topic of this artwork are new features of the well known Penrose tiling of the plane:

1. The precise geometric relation between quasi periodically spaced lines ("Ammann lines") and the tiling [1].

2. The corona limit of the tiling: Let a patch P of a Penrose tiling be a finite set of tiles. The n-th generation "immediate neighbours" of P, the n-th corona, scaled by 1/n, forms a decagon in the limit [2].

I thank Latham Boyle for his Mathematica program.

[1] L. Boyle, P. Steinhardt: Coxeter Pairs, Ammann Patterns and Penrose-like Tilings. arXiv: 1608.08215v2 31. Aug. 2016.

[2] S. Akiyama, K. Imai: The Corona Limit of a Penrose Tiling is a regular Decagon. Cellular Automata and discrete complex Systems, Springer 2016.