Tilings with 5 Prototiles
The Nischke-Danzer-Deltoid 7-fold-2-2 was discussed and derived in [ND96] but not shown. A figure with the tiling can be found in [Pau2017] .
Polytopal Tiles Self Similar Substitution Finite Local Complexity Finite Rotations Nischke Danzer Deltoid
A substitution tiling with six trapezoidal prototiles. The substitution rule is given for only five of the six tiles. The sixth tile (yellow) is substituted by nothing.
The discoverer gives credits to Veit Elser for suggesting the shape of the tiles.
The substitution tilings which are most relevant as models for physical quasicrystals are 5-fold, 8-fold, 10-fold and 12-fold symmetric ones. In the 5-fold (resp. 10-fold) case, there are the variations of the Penrose rhomb tilings and the Tuebingen triangle, for the 8-fold case there are the …
Denote the elements of the field $F_{4}$ by $\{0, 1, w, w + 1\}$, where $w$ satisfies the following equation with coefficients in $F_{2}: w^{2} + w + 1 = 0$.
Infinity is a recurrent double sequence defined by $a(i, 0) = a(0, j) = 1$ and $a(i, j) = f(a(i, j-1), a(i-1, j-1), a(i-1, j))$,
where $f(x, …
One of several substitution tilings found by L. Andritz using similar right-angled quadrilaterals.
One of several substitution tilings found by L. Andritz using similar right-angled quadrilaterals.
