Edge template - Revision history

Selinger: /* More edge templates */ Fixed link

2021-06-12T01:55:28Z

‎More edge templates: Fixed link

Selinger: Added link to ladder generation template

2020-12-17T17:58:21Z

Added link to ladder generation template

Selinger: Converted to new hexboard diagrams, added sections, copy-editing.

2020-12-08T00:42:34Z

Converted to new hexboard diagrams, added sections, copy-editing.

Wccanard: destubbed

2016-05-20T20:51:21Z

destubbed

Halladba: added to cat.edge templates and stub

2008-01-31T23:13:38Z

added to cat.edge templates and stub

Roland Illig: restored

2007-09-13T23:13:25Z

restored

Turing: reverted conent spam

2007-07-14T11:32:48Z

reverted conent spam

Gregorio: vandalism reverted

2007-06-11T10:53:11Z

vandalism reverted

Reiner Martin at 23:58, 7 June 2007

2007-06-07T23:58:46Z

Taral at 11:13, 28 March 2005

2005-03-28T11:13:04Z

@@ Line 79: / Line 79: @@
 * [[Edge templates with two adjacent stones]]
 * [[Edge templates with a bridge]]
-* [[Ladder generation template]]
+* [[Ladder creation template]]
 * [[Open problems about edge templates]]

@@ Line 79: / Line 79: @@
 * [[Edge templates with two adjacent stones]]
 * [[Edge templates with a bridge]]
 * [[Open problems about edge templates]]

@@ Line 1: / Line 1: @@
-An '''edge template''' is a [[pattern]] which guarantees a [[connection]] from a given stone to the [[edge]].
+An '''edge template''' is a minimal [[pattern]] that guarantees a [[virtual connection]] from a given stone, or sometimes several stones, to the [[edge]].
-Here is an example of an edge template ([[template IIIa]], also known as the ''Ziggurat''):
+== Example ==
-[[Image:Ziggurat.png]]
+Here is an example of an edge template ([[template IIIa]], also known as the [[ziggurat]]):
-<!-- <hex>R3 C4 Vc1 Sa1 Sb1 Sa2</hex> -->
+<hexboard size="3x4"
-The red stone on the third row has a certain connection to the bottom, using only the shaded hexagons, even if blue moves first. This is because (ignore the starred hexes, they are not part of the pattern) red is threatening either to play the piece marked 1
+The red stone on the third row has a certain connection to the bottom, using only the hexes that are shown, even if Blue moves first. This is because Red is threatening either to play at "A" and connect via the shaded area
 <hexboard size="3x4"
     coords="hide"
-    contents="E *:a1 E *:b1 R c1 E *:a2 R 1:b2 E +:a3 E +:b3"
+   edges="bottom"
     />
-and to connect via one the two hexes marked with a plus in the above diagram, or to play the piece marked 2
+or to play at "B" and connect via the shaded area
 <hexboard size="3x4"
     coords="hide"
-    contents="E *:a1 E *:b1 R c1 E +:d1 E *:a2 E +:c2 R 2:d2 E +:c3 E +:d3"
+   edges="bottom"
     />
-and to go on to connect by taking two of the hexes marked with a plus in this second diagram. Because these two escape routes for red do not overlap at all, red is guaranteed to be able to take one of them whatever blue plays next, and thus connect.
+Since these two escape routes for Red do not overlap at all, Red is guaranteed to be able to take one of them, no matter where Blue plays. Thus, Red is guaranteed a connection to the bottom edge.
-<!-- The [[Hex (board element)|cells]] marked by a star are irrelevant to the template, and can be occupied by either [[player]], or can be [[Empty hex|empty]]. Even if [[Blue (player)|Blue]] moves first, there is no way he can prevent from connecting to the [[bottom edge|bottom]]. -->
+== Minimality ==
-−
-Many edge templates are known. Some are very important and show up in many games; others are so big and unwieldy that they are of essentially no practical use and are just of interest to people such as those analysing the mathematical theory of hex.
-−
-An edge template is '''minimal''' if every hex in it is essential to the template -- in other words, if you remove a hex from the template then red is no longer guaranteed a connection. For example the Ziggurat is a minimal edge template; if we remove a hex from the template by marking it with an asterisk
 <hexboard size="3x4"
     coords="hide"
-    contents="E *:a1 E *:b1 R c1 E *:a2 E *:d3"
+   edges="bottom"
     />
+then Red can no longer connect if Blue moves first in this area:
-then red can no longer connect if blue moves first in this area:
 <hexboard size="3x4"
     coords="hide"
-    contents="E *:a1 E *:b1 R c1 E *:a2 R 4:b2 R 2:d2 B 5:a3 B 1:b3 B 3:c3 E *:d3"
+   edges="bottom"
     />
-Blue has established a line across the bottom edge and clearly red can no longer connect. There is no way through for red, if blue plays correctly.
+Blue has established a line across the bottom edge and clearly Red can no longer connect. There is no way through for Red, if Blue plays correctly.
-An edge template is a [[Edge templates with one stone|single stone template]] if it comprises only of one stone. The Ziggurat is an example of a single-stone edge template. There are many examples of edge templates which are not single-stone templates. For example the below pattern
+== Classification of edge templates ==
 <hexboard size="4x6"
     coords="hide"
-    contents="E *:a1 E *:b1 E *:c1 R 1:d1 E *:e1 E *:f1 E *:a2 E *:b2 R e2 E *:f2 E *:a3 R f3"
+   edges="bottom"
     />
-is a multiple-stone template. Red can connect their piece marked 1 to the bottom edge, even if it is blue's move. As usual the hexes marked with an asterisk are not part of the template. Here is an example of an attempt to block red's connection by blue, plus red's route around the attempted block.
+Red can connect their piece marked "↑" to the bottom edge, even if it is Blue's move. Here is an example of an attempt to block Red's connection by Blue, plus Red's route around the attempted block.
 <hexboard size="4x6"
     coords="hide"
-    contents="E *:a1 E *:b1 E *:c1 R d1 E *:e1 E *:f1 E *:a2 E *:b2 R 2:c2 B 1:d2 R e2 E *:f2 E *:a3 R 4:c3 R 6:d3 R 8:e3 R f3 B 3:b4 B 5:c4 B 7:d4 B 9:e4 R 10:f4"
+   edges="bottom"
     />
-Unsurprisingly, edge templates play a very important role in hex. Players who want to learn more of the basics about edge templates should now read [[Edge templates everybody should know]].
+== More edge templates ==
-On a theoretical level edge templates are interesting too. Here are some [[open problems about edge templates]].
+Many edge templates are known. Some are very important and show up in many games; others are so big and unwieldy that they are of essentially no practical use and are just of interest to people such as those analysing the mathematical theory of Hex.
 Other template pages on this wiki:
@@ Line 61: / Line 80: @@
 * [[Edge templates with a bridge]]
 * [[Open problems about edge templates]]
 [[category:edge templates]]

@@ Line 1: / Line 1: @@
-An '''edge template''' is a [[pattern]] which guarantees a [[connection]] the [[edge]].
+An '''edge template''' is a [[pattern]] which guarantees a [[connection]] from a given stone to the [[edge]].
-Here is an example of a [[Third row|third-row]] edge template ([[template IIIa]], also known as the ''Ziggurat''):
+Here is an example of an edge template ([[template IIIa]], also known as the ''Ziggurat''):
 [[Image:Ziggurat.png]]
@@ Line 7: / Line 7: @@
 <!-- <hex>R3 C4 Vc1 Sa1 Sb1 Sa2</hex> -->
-The red stone has a certain connection to the bottom, using only the shaded hexagons, even if blue moves first.
+The red stone on the third row has a certain connection to the bottom, using only the shaded hexagons, even if blue moves first. This is because (ignore the starred hexes, they are not part of the pattern) red is threatening either to play the piece marked 1
 <!-- The [[Hex (board element)|cells]] marked by a star are irrelevant to the template, and can be occupied by either [[player]], or can be [[Empty hex|empty]]. Even if [[Blue (player)|Blue]] moves first, there is no way he can prevent from connecting to the [[bottom edge|bottom]]. -->
-Countless edge templates can be constructed, all of them of varying degrees of usefulness and frequency of occurance.
+Many edge templates are known. Some are very important and show up in many games; others are so big and unwieldy that they are of essentially no practical use and are just of interest to people such as those analysing the mathematical theory of hex.
 * [[Edge templates everybody should know]]
@@ Line 17: / Line 60: @@
 * [[Edge templates with two adjacent stones]]
 * [[Edge templates with a bridge]]
 [[category:edge templates]]

← Older revision		Revision as of 23:13, 31 January 2008
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	* [[Edge templates with two adjacent stones]]		* [[Edge templates with two adjacent stones]]
	* [[Edge templates with a bridge]]		* [[Edge templates with a bridge]]
		+
		+	[[category:edge templates]]
		+	{{stub}}

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