Reading Wolfram’s “A New Kind of Science” to see what’s all the fuss about and I think he’s got the basics wrong.
For starters, his “cellular automata” do not produce #behavior but #structure, and all of the #complexity originates from the fact that every new row has two more pixels.
https://www.wolframscience.com/nks/p27–how-do-simple-programs-behave/
Conway’s “Game of Life” cellular automata can be said to produce #behavior as they maintain their initial dynamic #structure while moving through the “dead environment” of empty cells and will change their behavior when interacting with the static or dynamic structures of other “live” automatons.
“For starters, his “cellular automata” do not produce #behavior but #structure, and all of the #complexity originates from the fact that every new row has two more pixels.”
In physics, in a multi-dimensional extent where one of dimensions is time, then “structure” and “behavior” are two different terms that describe the same phenomenon.
Also, in cosmology the expansion of spacetime could be thought of as adding “more pixels”, so if the progression through the automata by adding new rows represents the progression through time, then it makes sense.
I’ll give you that you may have a #structure as a #record of how one or more (finite number of) variables change in time (#trajectories) describing some observed behavior, but this is not what Wolfram’s “pyramids” are. They look more like inverted sedimentation structures.
Also, as far as I understand cosmology, all the “pixels” in the expanding universe were there from the beginning. The expanding universe is not creating any new pixels as Wolfram’s automatons do.
Wolfram’s work with cellular automata is just one of many simple-rules-based approaches. His examples are very simple two-dimensional models to illustrate how complexity can emerge from simple rules. I don’t think he believes that a two-dimensional model could be used as an actual model for the representation of, e.g., spacetime or quantum phenomena.
Wolfram’s approach necessitates that spacetime is discrete. However, the expansion of spacetime is the expansion of the metric, the scale, so if that involves simply changing the scale of the quantized units of spacetime, then yes that would not involve “new pixels” and any concept of those “pixels” would need to be virtual for purposes of a model only. However if the expansion of spacetime includes the expansion of the quantity of discrete units then that would “add pixels”. In either case, whether the pixels are actual, or virtual only for the purposes of the model, it would still make sense. At least to me it makes sense.
@Kihbernetics Phew. A rather bold claim. Hope that someone will pick-up the ball.