Tiling |
Description |
Tiling Images |
Results |
Source Code |
CDF Demo * |
Comments |
AmmannA3 |
The Ammann A3 tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
The dimensions for the Ammann A3 tiling are found in Tilings and Patterns by B. Grunbaum and G. C. Shephard (Second, Edition, 2016). Images of 3D-printed stacked blocks for the tiling can be found here and here. |
|
AmmannA4 |
The Ammann A4 tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
The dimensions (and see here) for the Ammann A4 tiling are found in Tilings and Patterns by B. Grunbaum and G. C. Shephard (Second, Edition, 2016). |
|
AmmannChair |
The Ammann A2 chair tiling whose dimensions are described at this link. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
The dimensions for the Ammann chair tiling are found in Tilings and Patterns by B. Grunbaum and G. C. Shephard (Second, Edition, 2016). Images of 3D-printed stacked blocks for the tiling can be found here and here. |
AmmannChair2 |
A second 4-tile variation of the chair tiling described in this paper for comparison with the Ammann A2 chair tiling results. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
cdf |
|
AmmannEightStar |
Ammann-Beenker tiling for an initial 8-star tile. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
AmmannOctagon |
Ammann-Beenker tiling for an initial octagonal tile. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
AmmannRhomb |
Ammann-Beenker tiling for an initial rhomb tile. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
AmmannSquare |
Ammann-Beenker tiling for an initial square tile. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
AmmannTriangle |
Ammann-Beenker tiling for an initial triangular tile. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
Armchair |
A 4-tile L-shaped chair variant called the armchair tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Cesi |
An implementation of Cesi's substitution tiling. This tiling provides an example where the tiles occur in infinitely many orientations. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Chair3 |
The third (9-tile) chair tiling variant described here. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
cdf |
|
Danzer7Fold |
The original variation of Danzer's 7-fold tiling which exhibits 7-fold symmetry. See also this related Danzer tiling variant. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
DiamondTriangle |
The diamond triangle tiling which provides another example of a triangular-related substitution tiling for comparison with the results in the form below. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Domino |
The domino tiling described here. See also this related domino tiling variant. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
Domino-9Tile |
The 9-tile domino tiling variant. This substitution tiling is related to the imbalanced orientations tiling and is implemented similarly by an extension of the python source for this example. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Equithirds |
The equithirds tiling with triangle-shaped prototiles. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Fibonacci2D |
The two-dimensional Fibonacci times Fibonacci tiling, which is the Cartesian product of two of the famous one-dimensional Fibonacci tilings. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
GoldenTriangle |
The golden triangle tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
cdf |
|
GRTriangle |
The golden rhomboid triangle tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
IntegerLattice |
Implements an integer lattice in the first quadrant for testing purposes (\(1 < y < x \leq 350\)). |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
IntegerLattice3D |
Implements an integer lattice in the first octant for testing purposes (\(0 < z < y < x \leq 125\)). |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
MiniTangram |
A variant of the mini-tangram tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
cdf |
|
Octagonal1225 |
The octagonal 1-2-2-5 tiling which answers a question posed by L. Danzer of whether there is a substitution tiling with substituion matrix entries of 1-2-2-5. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
We used the square root of the largest eigenvalue, \(1 + \sqrt{2}\), of the substitution matrix, [ [1, 2], [2, 5]], to determine the scaling / inflation factors for this tiling implementation. |
PChairs |
Another chair tiling variant called the pregnant chairs (variant) tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Penrose |
The Penrose rhomb tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
PenroseKD |
The Penrose kite-dart tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Pentagon1 |
The first pentagon tiling from the demo described here. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
Pentagon2 |
The second pentagon tiling from the demo described here. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
Pentagon3 |
The third pentagon tiling from the demo described here. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
Pentagon4 |
The fourth pentagon tiling from the demo described here. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
Pentagon5 |
The fifth pentagon tiling from the demo described here. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
Pentagon8 |
The eighth pentagon tiling from the demo described here. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
Pentagon10 |
The tenth pentagon tiling from the demo described here. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
Pentagon11 |
The eleventh pentagon tiling from the demo described here. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
Pentagon15 |
The fifteenth pentagon tiling from the demo described here. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
[link][sagews] |
|
Pentomino |
A pentomino substitution tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Pinwheel |
The pinwheel tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
link |
|
SaddleConnGoldenL |
Statistics for saddle connections on the Golden L (see the gap distributions paper linked here). |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
SDHouse |
The semi-detached house substitution tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Sphinx |
The sphinx tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Squares |
A periodic squares mock tiling for comparison. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
STPinwheel |
A square triangle pinwheel tiling variant. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
T2000Triangle |
The limit-periodic T2000 triangle tiling involving 30-120-30 triangular tiles. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Tetris |
The first variant of the tetris substitution tiling in the Tilings Encyclopedia. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Triangles |
A periodic triangle mock tiling for comparison. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
Trihex |
A limit-periodic semi-hexagonal 30-60-90 triangular (trihex) tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
TriTriangle |
The tri-triangle tiling with triangular prototiles. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
|
TubingenTriangle |
The Tubingen triangle tiling with two isoceles triangular-shaped prototiles with edge length ratio of \(\varphi\):1:\(\varphi\) and 1:\(\varphi\):1 where \(\varphi \approx 1.618\) denotes the golden ratio. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
See also this article for more information about the gap distributions of this and several other tilings. This Sage script is used to study the symmetry groups of the Tubingen triangle and its orbits under the Hecke \((2, 5, \infty)\) triangle group. |
WaltonChair |
The Walton chair tiling. |
pdf
|
[angles]
[angle gaps]
[slopes]
[slope gaps]
[pc-edist]
[pc-edistsq]
|
Python source
|
X |
See this link for more information on the dimensions of this chair tiling variant. |