Examples
Basic Examples (3)
Plot a single hat tile:
Plot a hexagonal tiling of three layers of the Hat tiles:
Plot with combinatorial hexagon, the Hat, its supertile (cluster), 2-supertile and so on:
Scope (4)
Generate three different combinatorial equivalent tilings with two types of tiles:
There are 10 different initial conditions:
Compare with its supertiles:
You can generate any higher level supertiles as you want:
Options (5)
ColorFunction (1)
Add red EdgeForm in a blue tiling:
Count (2)
Use "Count" to generate more possible tilings:
Generate all valid one layer surroundings:
Properties and Relations (4)
HatHexagons (2)
The resource function HatHexagons generates tilings by substitution rule, which gives a fractal structure. HatHexagonalTiling focuses on surrounding the center tile by multiple layers. Compare the results of two functions after using the same initial conditions:
You can use this function to generate higher level supertiles of the Hat as a whole, and use HatHexagons to see how it is made of the hat tiles:
Supertiles (1)
The "Cluster" is exactly 1-Supertile, the "SuperCluster" is exactly 2-Supertile and the "Hat" is the "0-Supertile":
Reflected Tiles (1)
The holes in the Hat tiling are where the reflected tiles should be. An easy way to fill them is:
Possible Issues (3)
Duplicate elements in typelist will give duplicate corresponding results:
If you want to generate combinatorial tilings with different type of tiles, please use the typelist argument rather than Map. There is a significant efficiency difference:
They have the same result:
Neat Examples (1)
Show the two kinds of tiles next to the reflected tiles:
Publisher
Bowen Ping
Requirements
Wolfram Language 13.0
(December 2021) or above
Version History
-
1.1.2
– 08 May 2024
-
1.1.1
– 06 December 2023
-
1.1.0
– 04 December 2023
-
1.0.0
– 15 November 2023
Related Resources