Artists
Statement
I am a retired engineer, computer hobbyist, naive artist and have always been fascinated by geometry. 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 fun.
Artworks
In 2023 an “Einstein” was discovered, a single shape which tiles the plane aperiodically, “the hat” [1, link]. Here an arbitrary hat tile is surrounded by shells. Shell $S_n$ contains all tiles adjacent to $S_{n-1}$ that are not in $S_{n-2}$.
The growth form of a tiling can be informally defined as lim $S_n$ / $n$ for $n$ → ∞. Many non-periodic tilings, and also the hat tiling, have a growth form [2, 3]. We see its convergence to a regular hexagon.
[1] https://archive.bridgesmathart.org/2023/bridges2023-1.html.
[2] D. Demski, P. Hilgers, and A. Shutov. “Growth forms of grid tilings.” Acta Crystallographica A, vol. 78, no. 4, 2022, pp. 309-318.
[3] A. Shutov. Personal communication.