the most famous quasiperiodic tiling
The most famous example of aperiodic tilings are the Penrose tilings, named after Arthur Penrose, who investigated them in the 1970s. They can also be generated using the Cut-and-Project Method by choosing \(n=5\), \(\Lambda = \mathbb{Z}^n\) and \(E\) as a certain 3-dimensional affin-linear subspace. Although the procedure of the method is less graphically intuitiv in this higher dimension, you are also able to change the offset \(\gamma\) along a given 5-dimensional vector to obtain different results. In the interactive figure below you can do this yourself as well as zoom in and out and shift the axes to take a look at the interesting images created.
Play around with Zoom, Move X, Move Y and Offset to see how the
Penrose tiling changes. If you want to have a larger frames of your
current penrose tiling, you can click on the button below. Computing
can take some time, so don't worry.