I recently saw a video about Wolframs "new kind of science" and started to read the book, as a hobbyist in regards to cellular automata, that always wondered if cellular automata could be translated into a more basic graph structure I am very interested in wolframs idea about updating graphs.
Now I am also quite a fan of the idea of selfevolving code and I always wondered if one could not write a genetic algorithm for code, but alas I never had the expertise to programm an experiment for this, as I quickly realized that such an algorithm would need to be taught how to navigate the graph of a code's syntax.
Now if we had a ruleset for updating graphs that was computational universal, everything could be represented in the form of a graph and it should be much easier and natural to write a genetic algoritm able to operate on itself.
If such a ruleset was causal invariant, simulation would be even easier.
Such my question: what is simplest causal invariant and computational universal ruleset( if there are rulesets able to model the universe they also should be computational universal right?)
I don't know if this is quite what you are asking about, but there is the field of evolutionary programming. A good reference for this, using Mathematica, is
Jacob, C. Illustrating Evolutionary Computation with Mathematica. San Francisco, CA: Morgan Kaufmann, 2001.
There are perhaps more recent works in this area, quite possibly some by Christian Jacob. I should mention also that computer programs themselves are among many objects considered by evolutionary programming,
Whether or how this might be related to CA is another matter. I just wanted to point out that there is some existing body of work related to genetic-type operations on computer code, and moreover some of this literature involves use of Mathematica / Wolfram Language.
After some search : Meta-genetic programming and graph rewriting systems seem to be the two things I want to combine but both seem to require a hopelessly higher lvl of computer science education than I posses.
I know there are works out there relating to "code evolution" all I can come up with is far behind what brighter minds might already have figured, however like stated are those articles often so technical that you do not even know where to start understanding them and many of the required reading material is not exactly freely available.
I just think that as graphs can represent both data and code and as having fewer operations simplifies the searchspace for a genetic algorithm, trying meta genetic programming on graphs with an appropriate ruleset seems an obvious approach to me and something I could try to busy myself with.(If someone smarter than me provided the required ruleset ^^)