I think there are a couple of things about Wolfram's book which aren't well understood.

Most importantly, he is not specifically commited to cellular automata. He does focus on them, especially 1-dimensional, 2-state CAs, as a particularly simple model of computation, which also has the property that a relatively high percentage of randomly chosen programs produce apparent complexity. But he explores a number of other computational systems, including higher dimensional and higher state CAs; mobile CAs; Turing machines; substitution systems; sequential substitution systems; tag systems; cyclic tag systems; register machines; symbolic systems; arithmetic; recursive sequences; iterated maps; continuous (non-quantized) CAs; partial differential equations; network systems; multiway systems; constraint satisfaction systems; and higher dimension versions of many of these. The lesson he draws is that generally, the same kinds of patterns are seen in virtually all of these ways of expressing computation. You see simple, constant outputs; simple repetition; chaotic patterns; and occasionally, the mysterious "structure" on the edge of chaos, which often shows tantalizing particle-like phenomena and other interesting analogs to real-world phenomena. Where he does fall back on CAs, I don't think his point is so much that the phenomena are based precisely on CAs, but that random, simple algorithms when implemented in CAs often produce very similar patterns to what we see in the real world. And that this is probably not coincidence. It suggests that these kinds of patterns could be considered attractors in pattern space. They are easier to produce than other patterns that might seem superficially similar. Their algorithm complexity is lower. And this insight might inform our efforts to understand the true nature of the phenomena which create these patterns. Where Wolfram turns to physics, his speciality, he explicitly departs the CA model as he tries to sketch a possible mathematical basis for the universe that is consistent with the paradoxical phenomena of QM and relativity. He uses network systems, hypothetical sub-quantum "nodes" which are connected to one another and whose connections might change under simple rules. This is not completely original; I think Wheeler and others pursued ideas similar to this back in the 70s. Wolfram takes it a little farther in showing how you could get some relativity-style phenomena, but it's a very bare beginning effort. My main point is that characterizing Wolfram as saying that the universe is a CA, or biological patterns or fluid turbulence or any other phenomena are caused by CAs, is not correct. He is not saying these phenomena are caused by CAs, he is saying that extremely simple CA programs produce similar phenomena, suggesting that such phenomena emerge spontaneously from computational systems. As for the universe, I think his point is that the grand, mathematical elegance of string theory and similar methods is the wrong approach. These beautiful mathematical models are too rigid and brittle to describe a universe like ours. The universe is more likely to be built out of a messy, random and simple little program that just happens to create patterns that have the properties necessary for life to evolve. In the context of our list, this can be thought of as a philosophical bias towards Schmidhuber and away from Tegmark. In Tegmark's model, string theory is relatively near the origin of the tree of mathematical structure; it is simple. If it produced enough particles and interactions of the right kinds to allow for life, it would be an excellent candidate for the place where we live. But in Schmidhuber's model, it's just as likely that some random hodgepodge of a program a few thousand bits in length will "just happen" to produce a very robust, dynamic and varied universe with all kinds of structure at different size scales. Such a universe is an inherently friendly home for life as there are so many possible niches for it to grow. Of course, at this point we are in no position to decide between these two philosophies. Wolfram's book is ultimatly a call to our intuition, an appeal for equal time to be given to Schmidhuber-ish approaches based on random programs, as for the traditional Tegmarkian mathematical modelling which is done in physics. I think there is something to be said for this shift in perspective, and I hope that at least a small minority of researchers will attempt to move Wolfram's program forward. Hal Finney