Frédéric Lançon
Discovered Tilings
In [Lan88], energetic properties of certain decorations of Penrose Rhomb tilings were studied.
A $\frac{\pi}{5}$, $3\frac{\pi}{5}$}, or in {$2\frac{\pi}{5}$, $4\frac{\pi}{5}$}.
(‘Binary’ because …
Finite Rotations Polytopal Tiles Parallelogramm Tiles Rhomb Tiles Finite Local Complexity
The substitution can be expressed by using the real inflation factor $\sqrt{\tau} = 1.272\ldots$, where $\tau=\frac{\sqrt{5}+1}{2}$ is the golden mean. This factor is not a PV number. Nevertheless, the tiling is pure point diffractive, and it is a cut and project tiling, see [Gel97]
, [Dv00]
. Thus …
With Decoration Finite Rotations Polytopal Windowed Tiling Polytopal Tiles Self Similar Substitution
Also known as ’table tiling’. In [Sol97] was shown that its dynamical spectrum has a continuous component. Thus it cannot be a cut and project tiling. The same was shown in [Rob99] , where a topological model of the dynamical system of the domino tilings is obtained.
Polyomio Tiling Finite Rotations Polyomio Tilings Rep Tiles Self Similar Substitution