You didn’t quite mention “emergence” anywhere to now, but I believe emergence and pattern (structure) creation are phenomena inherent to all complex systems. In that sense I am with you on that randomly sampling the possible initial conditions of a discrete Markov chain and a continuous dynamical system, as described by equations in physics, can very well yield emergent complex patterns very comparable to each other.

Did you use simple linear regression? Or some other type of fit? Interesting.

Its dimensionality. And probably topology.

Is it 3D? I’m 99% sure of that. The interesting part is in the other 1%. Maldacena duality or the AdS/CFT correspondence seem to point in favor of the other hypothesis today. We’ll see soon, I believe, as more and more experimental discoveries sift through all the recent theories that emerged for our ontology…

Topologically, I don’t quite take it we are all living in a torically connected universe or one with structurally dodecahedric cells in a hyperbolic space, for instance, but wouldn’t it be great to discover somehow that similar structures might exist in a “neighboring” universe? I’m thrilled to find out what the next decade of discoveries will be with all those new instruments scheduled to launch very soon. The next 100 years, these expectations will scale up exponentially.