Tiling 
Description 
Tiling Images 
Results 
Source Code 
CDF Demo * 
Comments 
AmmannA3 
The Ammann A3 tiling. 
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 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 3Dprinted stacked blocks for the tiling can be found here and here. 
AmmannA4 
The Ammann A4 tiling. 
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 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. 
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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 3Dprinted stacked blocks for the tiling can be found here and here. 
AmmannChair2 
A second 4tile variation of the chair tiling described in this paper for comparison with the Ammann A2 chair tiling results. 
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AmmannEightStar 
AmmannBeenker tiling for an initial 8star tile. 
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AmmannOctagon 
AmmannBeenker tiling for an initial octagonal tile. 
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AmmannRhomb 
AmmannBeenker tiling for an initial rhomb tile. 
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AmmannSquare 
AmmannBeenker tiling for an initial square tile. 
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AmmannTriangle 
AmmannBeenker tiling for an initial triangular tile. 
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Armchair 
A 4tile Lshaped chair variant called the armchair tiling. 
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Cesi 
An implementation of Cesi's substitution tiling. This tiling provides an example where the tiles occur in infinitely many orientations. 
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Chair3 
The third (9tile) chair tiling variant described here. 
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Danzer7Fold 
The original variation of Danzer's 7fold tiling which exhibits 7fold symmetry. See also this related Danzer tiling variant. 
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DiamondTriangle 
The diamond triangle tiling which provides another example of a triangularrelated substitution tiling for comparison with the results in the form below. 
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Domino 
The domino tiling described here. See also this related domino tiling variant. 
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Domino9Tile 
The 9tile 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. 
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Equithirds 
The equithirds tiling with triangleshaped prototiles. 
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Fibonacci2D 
The twodimensional Fibonacci times Fibonacci tiling, which is the Cartesian product of two of the famous onedimensional Fibonacci tilings. 
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GoldenTriangle 
The golden triangle tiling. 
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GRTriangle 
The golden rhomboid triangle tiling. 
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IntegerLattice 
Implements an integer lattice in the first quadrant for testing purposes (\(1 < y < x \leq 350\)). 
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IntegerLattice3D 
Implements an integer lattice in the first octant for testing purposes (\(0 < z < y < x \leq 125\)). 
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MiniTangram 
A variant of the minitangram tiling. 
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Octagonal1225 
The octagonal 1225 tiling which answers a question posed by L. Danzer of whether there is a substitution tiling with substituion matrix entries of 1225. 
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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. 
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Penrose 
The Penrose rhomb tiling. 
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PenroseKD 
The Penrose kitedart tiling. 
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Pentagon1 
The first pentagon tiling from the demo described here. 
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Pentagon2 
The second pentagon tiling from the demo described here. 
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Pentagon3 
The third pentagon tiling from the demo described here. 
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Pentagon4 
The fourth pentagon tiling from the demo described here. 
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Pentagon5 
The fifth pentagon tiling from the demo described here. 
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Pentagon8 
The eighth pentagon tiling from the demo described here. 
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Pentagon10 
The tenth pentagon tiling from the demo described here. 
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Pentagon11 
The eleventh pentagon tiling from the demo described here. 
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Pentagon15 
The fifteenth pentagon tiling from the demo described here. 
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Pentomino 
A pentomino substitution tiling. 
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Pinwheel 
The pinwheel tiling. 
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SaddleConnGoldenL 
Statistics for saddle connections on the Golden L (see the gap distributions paper linked here). 
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SDHouse 
The semidetached house substitution tiling. 
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Sphinx 
The sphinx tiling. 
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Squares 
A periodic squares mock tiling for comparison. 
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STPinwheel 
A square triangle pinwheel tiling variant. 
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T2000Triangle 
The limitperiodic T2000 triangle tiling involving 3012030 triangular tiles. 
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Tetris 
The first variant of the tetris substitution tiling in the Tilings Encyclopedia. 
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Triangles 
A periodic triangle mock tiling for comparison. 
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Trihex 
A limitperiodic semihexagonal 306090 triangular (trihex) tiling. 
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TriTriangle 
The tritriangle tiling with triangular prototiles. 
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TubingenTriangle 
The Tubingen triangle tiling with two isoceles triangularshaped prototiles with edge length ratio of \(\varphi\):1:\(\varphi\) and 1:\(\varphi\):1 where \(\varphi \approx 1.618\) denotes the golden ratio. 
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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. 
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See this link for more information on the dimensions of this chair tiling variant. 