I guess I have to read the book, because I can't believe the above summary. If the above statement is true, the book is a gigantic hoax. First, becuase Wolfram's alleged "proof" was proved back in 1966 by Arbib. Secondly, because Deutch proved in 1985 that a "Turing Machine" could not simulate our actual universe. Indeed, it cannot even simulate a photon.
I grant that many of the forms we see in Nature could be the result of simple interactions iterated many times. But gee, that was first demonstrated in 1917, no less, in D'Arcy Thompson's magnificent book On Growth and Form.
In sum, nothing mentioned in the above review is in any way novel. So I guess I suspend judgement until I can read the whole thing.
From what I've read elsewhere, in 1985, Deutsch proved that a quantum computer can simulate any quantum system, including the Universe itself. He's quoted as saying "The set of all programs that can be run on a quantum computer includes programs that would simulate the multiverse ... so we don't have to include any details of stars and galaxies in the real Universe, we can just analyse quantum computers and look at how information flows inside them."
I don't know how to simulate the universe with a computer that is smaller than the universe, but a quantum computer is apparently the way to try. It seems relevant to cellular automata that most of the time, according to Deutch, information flows only within single universes of the quantum calculation, and not between those universes. This seems at first glance to contradict Tegmark, who has noted that the total amount of information in the multiverse is much less than in any that in any one universe taken alone.
This guy isn't claiming you can simulate the universe with a Turing machine. He says the universe IS a Turing machine.
BUMP