Fibonacci Times Fibonacci

Rule Image

The 2dim analogue of the famous Fibonacci tiling in one dimension. It is just the Cartesian product of two Fibonacci tilings F1, F2: {T1×T2 | Ti in Fi}. Obviously, it can be generated by a substitution with three prototiles.
It shares a lot of nice features with the 1dim Fibonacci tiling: It is a model set (better: it's mld with one), so it has pure point spectrum. Its window is just a square. Moreover, it is its own dual tiling. Trivially, it allows a decoration with Ammann bars.

Patch Image
»
Page Authors

Images: J. Pieniak
Text: D. Frettlöh