I appreciate this response. However the “cellular” is represented by the minimal computational data structure to simulate the gas. There is no automata. Ordinary physics, adhered to as closely as possible, and not phantasmagoric creation and annihilation rules, are used to calculate the next state.

I mean please don't take this answer the wrong way, but this is like saying "Some rich person should give away $1M for finding an application of complex numbers". It feels condescending. If your area deals with cellular automata e.g. programming languages, computer simulation, procedural generation etc applications of cellular automata are numerous and well understood. It's niche sure, but it's not like this entertaining thing that strangely has no practical applications. I downvoted GP because of this, since it assumes it has no applications and offers a rich person to help us out to compensate for that.

Disclosure: I worked on Mathematica for ~8 years.

I think the value of Stephen's big book is that served as a kind of manifesto to "take computation seriously". By that I mean: to think about computations, in the abstract, as a kind of new mathematics about which we know almost nothing, and about which our naive intuitions from other domains is almost totally inapplicable. It is an injunction to explore the "computational universe", in other words, the "universe of simple computational systems", where CAs live as one of several kinds of maximally simple form of computation (which Wolfram made some attempt to categorize and explore).

By analogy, think about the development of algebra. It didn't come naturally! Yet Algebra is one of the most natural ideas in abstract mathematics, incredibly simple and incredibly powerful, lying as a rosetta stone connecting so many other topics in mathematics. But people didn't immediately accept or describe it; it took many hundreds of years to crystalize and mature as a topic. It's a very old piece of the operating system of mathematics that underwent a lot of hacking and refactoring.

Wolfram proposes we think about computational systems in the same way, as a nascent field that needs exploration, mapping, the irrigation of young minds and new ideas. It may be some time before it yields a harvest. We shouldn't expect it to immediately revolutionize everything.

Even after Turing, computational systems existed as a kind of diaspora in mathematics, having sat unrecognized in all kinds of places, never having had a sort of independent state in which they are not considered as an aspect of something else, as somehow alien and unworthy of respect because of their confusing aspects. Largely, there were two reasons they were treated so shoddily:

1. they required computers (and good computer tools) to actually explore, since they produced complex and irreducible computations 2. they resisted any kind of analysis by prior mathematics

In other words, we were not ready to really probe them until a few decades ago, and even now our software is not well suited to explore them (Mathematica remains the best tool for the job, though I anticipate Julia will surpass it rapidly). Furthermore, traditional mathematical fields have not adapted to the presence of computation very gracefully.

I guess I would summarize: NKS is an imperfect book and Stephen an imperfect herald of the ideas within. But he was the first person to really articulate those ideas crisply and push them hard into the imagination, and I'm very glad he did. The hand he overplayed was the application to the natural world -- I think that will take longer to pay off than he predicted.

You should really take a look at the paper "Computation and Pattern Formation by Swarm Networks with Brownian Motion" or, more generally, any of the papers by Teijiro Isokawa and Ferdinand Peper. What they present is really close to (a theoretical version of) the microbots you're talking about.

I even wrote a report and presentation on those papers for university, but sadly they're in German.

The embryology of the brain is an obvious candidate. Very small instruction set to build it, the neuron pattern repeated, local rules and state.