Registered: Nov 2008
Posts: 39

Hello;

I have a project end studie about continous valued CA. it's to repeat again one shareware called CAPOW .

You know what that means. I must understand a lot of things like: neighbors, rules, states...

So, is it possible to extract all this just with looking to my aim, for example for this picture(ca.jpg), can i extract them, or it's impossible.


Or, for an expert, can he understand what all this structures means?

Otherwise, how can i arrive to do this. Please it's very important.

Thanks in advance.

M.Abdeldjalil has attached this image:

Last edited by M.Abdeldjalil on 02-26-2009 at 05:17 PM

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Registered: Nov 2008
Posts: 39

Hello,


I'm waiting for your help. Are there some people who can help me?

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Registered: Aug 2003
Posts: 712

Yes is it possible to infer all sorts of things from the CA evolution, without knowing the rule explicitly. With enough data you can figure it out. But it helps to have the actual values, not just an image. That way you can have the computer analyse the data explicitly, rather than guessing what the colors shown correspond to numerically, etc.

Reading in the picture in Mathematica using Import, I get an image that is 443 wide by 367 long, with 131152 distinct RGB color triples (out of 162581 total elements), with the most common triples occuring 10 times. These color triples presumably correspond to single real numbers in the original data, but the exact correspondance can't be inferred from the picture alone, without underlying real number values. There are multiple ways of going from a single real number site value to a given RGB triple. (An RGB triple is a color specified by one of 256 possible values, from 0 to 255, for each of three color channels, red, green and blue intensity). Moreover, jpg is a lossy compression scheme, so we do not actually know the underlying array had those dimensions in cells or that variety of distinct colors.

Just visually, several things are obvious. It is consistent with a range 1, 1D CA. This you can tell by the apparent speed of interaction across the pattern, reading the top of the picture as the first time step and time running down the page. The fact that structures seem to pass through one another (like interference patterns with waves) suggests an *additive* rule. The boundary conditions are clearly "wrapped", with the right edge connected to the left edge in "torus" fashion - the typical default boundary conditions for a finite-width CA evolution. Notice there isn't such wrapping between the top and the bottom of the picture - so the vertical is undoubtedly "time".

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Registered: Aug 2003
Posts: 712

With the actual data, how would one continue the analysis?

First we'd use our guess about the neighborhood size, derived from the apparent "light speed" of information flow in the pattern, to create local mapping instances. That is, we can partition the first row into groups of 3 cells and then associate those with the site value below them. And the same for the other rows. This gives us a huge number of local mapping instances of the form {a,b,c} -> d. When the actual numbers are known (rather than each of these being rough color-scheme triples), it should be relatively straightforward to infer the function itself from so many data points. Especially with the clue that it is probably additive (or "mod" additive, perhaps involving a fractional part or multiplicative factor etc).

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