Shifting Patterns

I don't know if the title of the page, and the name of the concept is correct. But after reading SmallestGroupWithTwoEyes, this reminds me some thoughts I had about transformation of stone patterns when they are shifted toward the edge or the corner. A quick search of "shifting" giving nothing, here is the page. It is a starting point and waits for comments and improvments (likely linguistic ones!)
GillesArcas

Concept

Shifting a pattern consists of examining what happens to a pattern located in the center of the goban when it is shifted toward the edge or the corner. Example:

 

When shifted to the North until the edge, it becomes:

 

And shifting this one to the East, this gives:

 

In the following, application to living shapes, snap, ko and seki is presented.

Such a concept could have no interest. But at least, it can be useful for:

• Pattern classification (see Diagonal eye shapes)
• Pattern creation (the central pattern presented for seki has been created from the corner position)
• Analysis tool to understand the technics used for related shapes

Shifting Diagonal eye patterns

Definition of diagonal eye patterns

Diagonal eye pattern patterns are absolute living shape with two eyes in diagonal position:

 

To become a living shape, two conditions must be fulfilled:

• the horizonal and vertical neighbour intersections must be of the same color:

 

• two diagonal neighbour intersections (in three free for the moment) for each eye must be of the same color. For instance:

 

Combining three possibilities for each eye, and pruning with symmetry, this leads to the 4 center groups in SmallestGroupWithTwoEyes.

Shifting diagonal eye shape

Following the terminology of SmallestGroupWithTwoEyes, here are all the shifting transformations, preserving life, of the diagonal eye patterns.

First center group  

Second center group  

Third center group  

Fourth center group  

Note that this one without any symetry can shift into all the center and corner diagonal eye patterns.

Shifting a seki pattern

Shifting can also be applied to seki patterns, for instance this one:

 

Shifted to the North-East corner, it gives the following shape:

 

and to the South-East corner, it gives this one:

 

Shifting a snap back pattern

Shifting can also be applied to standard tesuji shapes, like snap back.

 

Shifting the ko pattern ^[1]

 

Shifting life & death positions

Black to live

 

Black to live

 

Patterns can change their character when shifted.

Bent four shifted  

The center bent four eye shape is alive, but when it is shifted to the corner, Black to play can make a ko.

[1] After a post of Simon Goss on rgg.