Jason Cawley
Wolfram Science Group
Phoenix, AZ USA
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 finitewidth 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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