Wang Tiles

Wang Tiles (or Wang dominoes) are a class of formal mathematical systems first proposed by Hao Wang in 1961. They consist of equal-sized square tiles with colored edges that are arranged side-by-side on a regular grid.

When placing tiles to cover an infinite plane, you must strictly follow three structural constraints:

• Orientation: Tiles must be placed with a fixed orientation and cannot be rotated or reflected.
• Edge Matching: Adjoining edges of touching tiles must share the exact same color.
• Grid Alignment: Every tile must occupy exactly one square in a standard square grid.

Busy Beaver function

Define the score of a set of Wang tiles as the largest d such that it can tile a dxd square, or 0 if there is no largest d.

Then BB_WT(n) = the maximum score over all n-tile sets.

n	Value	Champion
1	1	TODO
2	2	TODO
3	3	TODO
4	≥ 4	TODO
5	≥ 6	TODO
6	≥ 8	TODO