Re: [computer-go] Fractals, was Search = Bad!

[Matt Gokey <mgokey@xxxxxxxxxxx>]

Just some additional musings about this topic as I think I now 
understand the basic premise.  Thanks David.

I am a long time believer in the multiple level/nested relationships 
model to playing computer-go.  I've never really thought of this concept 
applied to go as a fractal, however.

To me the key to fractal property is self-similarity at different 
scales.  Normally I think of fractals as existing in a spatial 
dimensional form of some kind.  In this case we're not talking about a 
spatial order, although a multitude of various mappings to a spatial 
format can be achieved (like John Tromp's picture of Connect-4).

The distance property between 2 points in this "fractal" space does not 
represent length distance between stones, but distance in plies or 
depth.  It is truly simply the game tree still in my mind.  But is it 
fractal in nature?  That depends on whether there exist patterns at 
different size scales within this space that are self-similar.  It is 
not at all evident to me that it is a fractal by this definition.

And if so, whether these self-similar patterns could be exploited to 
choose better moves in general is the other question.  Exploited via 
algorithmic, heuristic, or mathematical methods.  I think this is what 
David means by using scaling relationships to choose moves.  It is also 
not evident to me that this would work very well with the nuance of 
shape and stone relationships to tactical considerations.  At best, I 
can't see this working as well as standard pattern matching techniques.

David correct me if I've led myself astray and please comment on these 
thoughts if you will.

I don't know whether this characterization of the fractal idea matches 
what Frank was saying or not, however.  He asserts much more certainty 
over the fractal metaphor and potential techniques to navigate the 
"fractal" space than seems logical without any/much evidence.

Matt

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