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

[<wing@xxxxxxxx>]

I want to defend the fractal metaphor.

Mandelbrot defined many fractal relationships
that have inner and outer cutoffs. For example,
the coastline of Great Britain is a fractal which
has an inner cut-off at a grain of sand (perhap 1 mm),
and an outer cutoff at the size of the island (perhaps
1000 km). All scales in between have a fractal
relationship. All scales beyond these cutoffs
are meaningless.

The Mandelbrot set has no inner cutoff, so it is infinite.
But, there are many, many finite fractal relationships.

----

The real question about fractals is whether there are
scaling relationships in go games. Since saying "fractal"
is about as general as saying "linear" there are bound
to be many. The number of points in an area is very
linear. I believe that the nested "problems within
problems" of evaluting a position is a fractal.

When I think about the next move, I *try* to organize
problems so that some problems are parts of other
problems, which seems very fractal to me. Though, I don't
know of any computer program that organize problems like
that, it might be useful to do so.

The linear POVs in go are still hard enough and useful
enough to make the fractals seem either unnecessary or
useless. But, I suspect that fractals will eventually
prove very useful.

Michael Wing


> > > Your go fractal space theory and the restated theoretical goal to 
reach 
> > > the end of the fractal in a favorable place (for you) is just that - a 
> 
> Fractals are infinite structures. Mandelbrot set does not have an edge.
> Reaching the end is meaningles.
> 
> Of course, I guess we are assuming an approximation. Even in this case
> I am having a problem with this suggestion. The fact that mandelbrot set is
> generated by simple rules does not entail that there may be simple or 
complex
> set of rules which will help analyze its structure. Same with Conway's 
Life. 

_______________________________________________
computer-go mailing list
computer-go@xxxxxxxxxxxxxxxxx
http://www.computer-go.org/mailman/listinfo/computer-go/