Spightonians/ Discussion

Sub-page of Spightonians

Should the term include captures?

Tom:I like the name!

I was going to suggest that the five-position situation should be considered both before and after the move. However, on reflection, it is very often the case that the fact of a capture is much more important than whether an empty triangle is made at the same time. So I suggest that it should be assumed that no capture is made for a Spightonian. This is pretty much what you have done, except that it would eliminate the final Spightonian, leaving 20.

(Sebastian:) You are right that when captures come into play, the distinction about what was there before becomes a bit moot. We could write this in the introducting paragraph. However, I would rather keep the name "Spightonian" for all 21 geometrically possible patterns - just as the [ext] periodic table ends with elements that hardly ever are realized.

New Spightonians?

Tom: Is there a reason that you haven't included the 'throw in'?

(Sebastian:) "throw in" seems to refer more to a tactical purpose of a move rather than a specific move shape itself. Could you draw the Spightonian for what you have in mind?

Borders

(Sebastian:) How do we include moves at the edge of the board in this list?

[Diagram]
Close to the border  
[Diagram]
mirrored  

Can we replace the border with mirrored points like this?

Missing Spightonians?

I (Malcolm) only counted 20 diagrams. Also, I didn't see the following diagrams :

[Diagram]
Ripped keima  
[Diagram]
Ripped keima plus one stone  


Maybe I'm missing something.

(Sebastian:) The _ripped keima_ is a subclass of the tap (touching 1 enemy and 1 friend). But the _ripped keima plus one stone_ belongs to a class which I did indeed not list: touching 1 enemy and 2 friends. There are 6 such classes; I only listed classes that either already have names, or that contain important subclasses. There are more diagrams than listed classes, because some of them illustrate subclasses.

I see how it is confusing that I didn't mention that the page doesn't list all classes, so let's prepare a table. There are 15 different [ext] multisets with cardinality 4 of B, W and empty spaces. 6 of these (such as the tap and the thrust) have 2 different possible arrangements for the same number of stones. (These are the ones in which at least one element - either B, W, or empty space - has exactly 2 memberships.) I will call the two related arrangements "ortho-" and "para-", in analogy to the nomenclature for [ext] arene substitution patterns. In ortho-patterns, the dual-members occupy orthogonally adjacent places; in para-patterns, they occupy opposite places.

This gives us the following table of all possible classes. I indicated the unnamed patterns with systematic names in parentheses. If there is only one name in a cell, then there is no distinction between ortho- and para- patterns.

 B (arrangement) \ W |       0       |       1       |       2       |       3       |       4      |
 ----------------------+---------------+---------------+---------------+---------------+--------------+
 0 (ortho-)            | untouched     | touch         | carve         | (3e0f)        | gouge        |
 0 (para-)             |               |               | general wedge |               |              |
 ----------------------+---------------+---------------+---------------+---------------+--------------+
 1 (ortho-)            | narabi        | tap           | chop          | sashikomi     |
 1 (para-)             |               | thrust        | impinge       |               |
 ----------------------+---------------+---------------+---------------+---------------+
 2 (ortho-)            | straddle      | (1e2f.o)      | (2e2f.o)      |
 2 (para-)             | botsugi       | (1e2f.p)      | division      |
 ----------------------+---------------+---------------+---------------+
 3                     | (0e3f)        | (1e3f)        |
 ----------------------+---------------+---------------+
 4                     | fill          |
 ----------------------+---------------+

Spightonians/ Discussion last edited by Sebastian on June 8, 2010 - 22:18
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