## Ghost Diagrams

From: "andrew cooke" <andrew@...>

Date: Fri, 4 May 2007 09:32:14 -0400 (CLT)

http://www.logarithmic.net/ghost.xhtml

Need to check this out after work.  Some kind of search with backtracking,
I think.

Andrew

### Excellent

From: "andrew cooke" <andrew@...>

Date: Sun, 23 Nov 2008 11:10:52 -0300 (CLST)

So, over a year later, I finally do look at this in some detail.  It
really is very good.

Turns out that some time ago I explored something similar, but without the
generality (in particular, without Aa edges and without the elegant
approach to specifications, the nice "real time" backtracking display, or
the idea of power law backtracking).  I don't have the images or code any
more, but I do have a few framed prints hanging...

Clicking through the various provided "populations" (maybe genomes is a
better description) raises some obvious questions/observations.  These
tend to be related to invariants that the local rules embody, but which
the backtracking search is unaware of.

Fro example, http://www.logarithmic.net/ghost.xhtml?3333&3+1+&33++ shows
that there must be an even number of "1" within any closed region (zoom
out and you'll soon see the backtracking going crazy).  And
http://www.logarithmic.net/ghost.xhtml?3333&3+1+&33++# suggests that you
can have rules that impose global constraints (blocking half the plane,
for example).

That leads to questions about higher dimensions.  In 3D it seems to me
that we have another way (perhaps not very useful) of looking at the
protein folding problem (and, vaguely related, it's impossible not to
think of DNA here -
http://www.logarithmic.net/ghost.xhtml?abA+&B+C+&B+c+&B+D+&B+d+)

There are more thoughts (Feynman diagrams(!), k-morphisms and the relation
to cellular automata) in chapter 7 of the thesis.

Sweet.

Andrew

PS  Much of the thesis is related more to pixel-based textures; this work
is addressed mainly in chapter 7.