Although the original article bombastically announces how this could prove that the Universe is a simulation, some questions arise: what is really a simulation? Does having a bunch of rules by which the Universe behaves qualifies the same as a simulation? Nevertheless, I find this an interesting and inspiring read. It makes me wonder whether we can have a magic box that spits out all the correct answers about the Universe, characteristically without letting us know how and why are those answers correct. Following this line of thought, the next important step in machine learning could be extracting exact reasoning of the magic box in a way understandable to humans.
I think your perspective of a computational universe is of a rule-based program, however, another approach of a computational universe can be based on a chaotic process that is free from complex rules. In other words, simple processes, e.g. two standing waves interfere with one another can converge to some stable state. Fundamentally the concept actually becomes simply the exchange of information which is what the stand waves example boils down two. Indeed this is what we see in nature right down to the subatomic level. Atoms exchange information which then leads to a rendering of the physical juxtaposition of particles! Effectively that is a function; inputs are force carriers that atoms absorb and the output is the physical positioning of material, albeit atoms have quirky behaviors of what is considered a juxtaposition (super-position) but, nonetheless, positions are constrained effectively becoming a consistent pattern! So the rules of nature end up emerging from chaotic interactions that are simply driven by the exchange of information. Now realize that because the universe is composed of limited resources called information, where the distribution of such information, field densities, cause constraints that limit the influence of reactions(information exchanges) that leads to or forces the formation of structures.
Since any reality is based on information and information is intrinsically mathematical(state-driven) such realities, universes, will fall into patterns that, at least in this universe, humans interpret as rules.
