If you model the dynamics of astrophysical objects and increase the number of moving parts, the Schrödinger equation emergeshttp://www.sci-news.com/astronomy/astronomical-objects-schroedinger-equation-05786.html …
The dynamics observable in our universe might simply be the set of all stable differentiable automata that we can see emerge at low dimensionality (higher dimensions suffer more from scarcity of elements, are more difficult to measure and model, and may even lack stable dynamics)
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The universe is information preserving, so it cannot easily be stochastic. Randomness is easier to explain as unpredictability.
End of conversation
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