Wang Tiles - Revision history

HelpMe: Undo revision 10354 by Polygon (talk). and then add some stuff.

2026-11-07T15:55:11Z

Undo revision 10354 by Polygon (talk). and then add some stuff.

← Older revision		Revision as of 15:55, 7 November 2026
Line 54:		Line 54:
	\|16<ref name="YeyitoWTRocq" />		\|16<ref name="YeyitoWTRocq" />
	\|<code>[4,0,3,0] [3,0,4,1] [3,1,3,2] [5,2,4,0] [4,1,4,2] [4,1,3,1] [3,2,5,0]</code><ref name="YeyitoWTdcannounce">https://discord.com/channels/960643023006490684/1529586687926210691/1567754354671493152</ref>		\|<code>[4,0,3,0] [3,0,4,1] [3,1,3,2] [5,2,4,0] [4,1,4,2] [4,1,3,1] [3,2,5,0]</code><ref name="YeyitoWTdcannounce">https://discord.com/channels/960643023006490684/1529586687926210691/1567754354671493152</ref>
	\|		\|[[File:BusyBeaverWangTiles CurrentChampion 7.png\|alt=The best known champion for the largest valid square patch (16 by 16) made by a set of 7 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|8		\|8
	\|≥ 17<ref name="YeyitoWTRocq" />		\|≥ 17<ref name="YeyitoWTRocq" />
	\|<code>[4,0,3,0] [3,0,4,1] [3,1,3,2] [5,2,4,0] [4,1,4,2] [4,1,3,1] [3,2,5,0] [0,0,3,1]</code><ref name="YeyitoWTdcannounce" />		\|<code>[4,0,3,0] [3,0,4,1] [3,1,3,2] [5,2,4,0] [4,1,4,2] [4,1,3,1] [3,2,5,0] [0,0,3,1]</code><ref name="YeyitoWTdcannounce" />
	\|		\|[[File:BusyBeaverWangTiles CurrentChampion 8.png\|alt=The best known champion for the largest valid square patch (17 by 17) made by a set of 8 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|9		\|9

Polygon: /* Busy Beaver function */ removed outdated images for 7 and 8

2026-11-07T15:12:30Z

Busy Beaver function: removed outdated images for 7 and 8

← Older revision		Revision as of 15:12, 7 November 2026
Line 54:		Line 54:
	\|16<ref name="YeyitoWTRocq" />		\|16<ref name="YeyitoWTRocq" />
	\|<code>[4,0,3,0] [3,0,4,1] [3,1,3,2] [5,2,4,0] [4,1,4,2] [4,1,3,1] [3,2,5,0]</code><ref name="YeyitoWTdcannounce">https://discord.com/channels/960643023006490684/1529586687926210691/1567754354671493152</ref>		\|<code>[4,0,3,0] [3,0,4,1] [3,1,3,2] [5,2,4,0] [4,1,4,2] [4,1,3,1] [3,2,5,0]</code><ref name="YeyitoWTdcannounce">https://discord.com/channels/960643023006490684/1529586687926210691/1567754354671493152</ref>
	\|~~[[File:BusyBeaverWangTiles CurrentChampion 7.png\|alt=The best known champion for the largest valid square patch (11 by 11) made by a set of 7 Wang tiles.\|border\|center\|frameless]]~~		\|
	\|-		\|-
	\|8		\|8
	\|≥ 17<ref name="YeyitoWTRocq" />		\|≥ 17<ref name="YeyitoWTRocq" />
	\|<code>[4,0,3,0] [3,0,4,1] [3,1,3,2] [5,2,4,0] [4,1,4,2] [4,1,3,1] [3,2,5,0] [0,0,3,1]</code><ref name="YeyitoWTdcannounce" />		\|<code>[4,0,3,0] [3,0,4,1] [3,1,3,2] [5,2,4,0] [4,1,4,2] [4,1,3,1] [3,2,5,0] [0,0,3,1]</code><ref name="YeyitoWTdcannounce" />
	\|~~[[File:BusyBeaverWangTiles CurrentChampion 8.png\|alt=The best known champion for the largest valid square patch (14 by 14) made by a set of 8 Wang tiles.\|border\|center\|frameless]]~~		\|
	\|-		\|-
	\|9		\|9

Polygon: /* Busy Beaver function */ referenced BB_WANG(10)

2026-11-07T12:40:54Z

Busy Beaver function: referenced BB_WANG(10)

← Older revision		Revision as of 12:40, 7 November 2026
Line 67:		Line 67:
	\|-		\|-
	\|10		\|10
	\|≥ 212		\|≥ 212<ref name="JeandelRao2021">Emmanuel Jeandel, Michaël Rao, "[https://arxiv.org/pdf/1506.06492 An aperiodic set of 11 Wang tiles]". January 2021. Accessed 7 November 2026.</ref>
	\|		\|
	\|		\|

Polygon: Updated

2026-11-07T12:37:21Z

Updated

← Older revision		Revision as of 12:37, 7 November 2026
Line 42:		Line 42:
	\|-		\|-
	\|5		\|5
	\|≥ 6		\|6<ref name="YeyitoWTRocq">Yeyito, "[https://github.com/Yeyito777/bbchallenge-discoveries/blob/main/wang-tiles/rocq/wang/README.md BB_WT in Rocq: BB_WT(5) = 6, BB_WT(6) = 8, BB_WT(7) = 16, BB_WT(8) ≥ 17]". Github document, November 2026. Accessed 7 November 2026.</ref>
	\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,6,1,5] [4,5,2,6]</code>		\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,6,1,5] [4,5,2,6]</code>
	\|[[File:BusyBeaverWangTiles CurrentChampion 5.png\|alt=The best known champion for the largest valid square patch (6 by 6) made by a set of 5 Wang tiles.\|border\|center\|frameless]]		\|[[File:BusyBeaverWangTiles CurrentChampion 5.png\|alt=The best known champion for the largest valid square patch (6 by 6) made by a set of 5 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|6		\|6
	\|≥ 8		\|8<ref name="YeyitoWTRocq" />
	\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0] [5,7,1,6] [5,6,2,7]</code>		\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0] [5,7,1,6] [5,6,2,7]</code>
	\|[[File:BusyBeaverWangTiles CurrentChampion 6.png\|alt=The best known champion for the largest valid square patch (8 by 8) made by a set of 6 Wang tiles.\|border\|center\|frameless]]		\|[[File:BusyBeaverWangTiles CurrentChampion 6.png\|alt=The best known champion for the largest valid square patch (8 by 8) made by a set of 6 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|7		\|7
	\|~~≥ 11~~		\|16<ref name="YeyitoWTRocq" />
	\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0] [5,7,1,6] [5,6,2,7] [4,6,3,7]</code>		\|<code>[4,0,3,0] [3,0,4,1] [3,1,3,2] [5,2,4,0] [4,1,4,2] [4,1,3,1] [3,2,5,0]</code><ref name="YeyitoWTdcannounce">https://discord.com/channels/960643023006490684/1529586687926210691/1567754354671493152</ref>
	\|[[File:BusyBeaverWangTiles CurrentChampion 7.png\|alt=The best known champion for the largest valid square patch (11 by 11) made by a set of 7 Wang tiles.\|border\|center\|frameless]]		\|[[File:BusyBeaverWangTiles CurrentChampion 7.png\|alt=The best known champion for the largest valid square patch (11 by 11) made by a set of 7 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|8		\|8
	\|≥ 14		\|≥ 17<ref name="YeyitoWTRocq" />
	\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0] [5,0,6,0] [6,8,1,7] [6,7,2,8] [5,7,3,8]</code>		\|<code>[4,0,3,0] [3,0,4,1] [3,1,3,2] [5,2,4,0] [4,1,4,2] [4,1,3,1] [3,2,5,0] [0,0,3,1]</code><ref name="YeyitoWTdcannounce" />
	\|[[File:BusyBeaverWangTiles CurrentChampion 8.png\|alt=The best known champion for the largest valid square patch (14 by 14) made by a set of 8 Wang tiles.\|border\|center\|frameless]]		\|[[File:BusyBeaverWangTiles CurrentChampion 8.png\|alt=The best known champion for the largest valid square patch (14 by 14) made by a set of 8 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
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	== Analysis ==		== Analysis ==
	TODO		TODO

			== References ==

	[[Category:Functions]]		[[Category:Functions]]
	[[Category:Stubs]]		[[Category:Stubs]]

Elgan65536: Add text notation for champions 7, 8, and 9

2026-10-03T16:14:54Z

Add text notation for champions 7, 8, and 9

← Older revision		Revision as of 16:14, 3 October 2026
Line 53:		Line 53:
	\|7		\|7
	\|≥ 11		\|≥ 11
	\|		\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0] [5,7,1,6] [5,6,2,7] [4,6,3,7]</code>
	\|[[File:BusyBeaverWangTiles CurrentChampion 7.png\|alt=The best known champion for the largest valid square patch (11 by 11) made by a set of 7 Wang tiles.\|border\|center\|frameless]]		\|[[File:BusyBeaverWangTiles CurrentChampion 7.png\|alt=The best known champion for the largest valid square patch (11 by 11) made by a set of 7 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|8		\|8
	\|≥ 14		\|≥ 14
	\|		\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0] [5,0,6,0] [6,8,1,7] [6,7,2,8] [5,7,3,8]</code>
	\|[[File:BusyBeaverWangTiles CurrentChampion 8.png\|alt=The best known champion for the largest valid square patch (14 by 14) made by a set of 8 Wang tiles.\|border\|center\|frameless]]		\|[[File:BusyBeaverWangTiles CurrentChampion 8.png\|alt=The best known champion for the largest valid square patch (14 by 14) made by a set of 8 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|9		\|9
	\|≥ 17		\|≥ 17
	\|		\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0] [5,0,6,0] [6,0,7,0] [7,9,1,8] [7,8,2,9] [6,8,3,9]</code>
	\|[[File:BusyBeaverWangTiles CurrentChampion 9.png\|alt=The best known champion for the largest valid square patch (17 by 17) made by a set of 9 Wang tiles.\|border\|center\|frameless]]		\|[[File:BusyBeaverWangTiles CurrentChampion 9.png\|alt=The best known champion for the largest valid square patch (17 by 17) made by a set of 9 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-

Polygon: /* Busy Beaver function */ proper subscript

2026-08-23T10:43:34Z

Busy Beaver function: proper subscript

← Older revision		Revision as of 10:43, 23 August 2026
Line 11:		Line 11:
	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.		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.		Then BB<sub>WT</sub>(n) = the maximum score over all n-tile sets.

	The current format to describe a set of tiles is a list of tuples that have 4 nonegative numbers, each representing a side color. Example: <code>[TOP,RIGHT,BOTTOM,LEFT]</code>		The current format to describe a set of tiles is a list of tuples that have 4 nonegative numbers, each representing a side color. Example: <code>[TOP,RIGHT,BOTTOM,LEFT]</code>

HelpMe: colorful images

2026-08-15T04:00:54Z

colorful images

← Older revision		Revision as of 04:00, 15 August 2026
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	!Value		!Value
	!Champion		!Champion
			!Image
	\|-		\|-
	\|1		\|1
	\|1		\|1
	\|<code>[1,0,0,0]</code>		\|<code>[1,0,0,0]</code>
			\|[[File:BusyBeaverWangTiles CurrentChampion 1.png\|alt=The definite champion for the largest valid square patch (1 by 1) made by a set of 1 Wang tile.\|border\|center\|frameless]]
	\|-		\|-
	\|2		\|2
	\|2		\|2
	\|<code>[1,0,2,0] [2,0,3,0]</code>		\|<code>[1,0,2,0] [2,0,3,0]</code>
			\|[[File:BusyBeaverWangTiles CurrentChampion 2.png\|alt=The definite champion for the largest valid square patch (2 by 2) made by a set of 2 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|3		\|3
	\|3		\|3
	\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0]</code>		\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0]</code>
			\|[[File:BusyBeaverWangTiles CurrentChampion 3.png\|alt=The definite champion for the largest valid square patch (3 by 3) made by a set of 3 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|4		\|4
	\|4		\|4
	\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0]</code>		\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0]</code>
			\|[[File:BusyBeaverWangTiles CurrentChampion 4.png\|alt=The definite champion for the largest valid square patch (4 by 4) made by a set of 4 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|5		\|5
	\|≥ 6		\|≥ 6
	\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,6,1,5] [4,5,2,6]</code>		\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,6,1,5] [4,5,2,6]</code>
			\|[[File:BusyBeaverWangTiles CurrentChampion 5.png\|alt=The best known champion for the largest valid square patch (6 by 6) made by a set of 5 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|6		\|6
	\|≥ 8		\|≥ 8
	\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0] [5,7,1,6] [5,6,2,7]</code>		\|<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0] [5,7,1,6] [5,6,2,7]</code>
			\|[[File:BusyBeaverWangTiles CurrentChampion 6.png\|alt=The best known champion for the largest valid square patch (8 by 8) made by a set of 6 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|7		\|7
	\|≥ 11		\|≥ 11
	\|		\|
			\|[[File:BusyBeaverWangTiles CurrentChampion 7.png\|alt=The best known champion for the largest valid square patch (11 by 11) made by a set of 7 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|8		\|8
	\|≥ 14		\|≥ 14
	\|		\|
			\|[[File:BusyBeaverWangTiles CurrentChampion 8.png\|alt=The best known champion for the largest valid square patch (14 by 14) made by a set of 8 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|9		\|9
	\|≥ 17		\|≥ 17
	\|		\|
			\|[[File:BusyBeaverWangTiles CurrentChampion 9.png\|alt=The best known champion for the largest valid square patch (17 by 17) made by a set of 9 Wang tiles.\|border\|center\|frameless]]
	\|-		\|-
	\|10		\|10
	\|≥ 212		\|≥ 212
			\|
	\|		\|
	\|}		\|}

Azerty: /* Busy Beaver function */ Improved lower bounds.

2026-08-14T15:41:43Z

Busy Beaver function: Improved lower bounds.

← Older revision		Revision as of 15:41, 14 August 2026
Line 45:		Line 45:
	\|-		\|-
	\|7		\|7
	\|≥ 10		\|≥ 11
	\|		\|
	\|-		\|-
	\|8		\|8
	\|≥ 12		\|≥ 14
	\|		\|
	\|-		\|-
	\|9		\|9
	\|≥ 14		\|≥ 17
	\|		\|
	\|-		\|-

Azerty: /* Busy Beaver function */ Added more lower bounds.

2026-08-14T15:38:55Z

Busy Beaver function: Added more lower bounds.

@@ Line 43: / Line 43: @@
 |≥ 8
 |<code>[1,0,2,0] [2,0,3,0] [3,0,4,0] [4,0,5,0] [5,7,1,6] [5,6,2,7]</code>
 |}

C1: Complemented the stub tag.

2026-08-13T09:00:27Z

Complemented the stub tag.

← Older revision		Revision as of 09:00, 13 August 2026
Line 1:		Line 1:
			{{Stub}}
	'''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.		'''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.