Regarding In-form-ation Flow and Density
In finding paths or routes a standard approach is to do some kind of uniform metric or a continuous function constraint metric (a smooth and continuous gradient) combined with a deterministic or stochastic search algorithm.
In the quantum world a problem occurs such that quantum mechanics calculation must be employed using either a Hamiltonian or a Lagrangian formalism. The quantum of complex numbers (C is a complete field) paths (wave functions), adding them together is called a superposition. The square being interpreted as a (positive) probability (implicitly continuous). There is a similar problem with general relativity on the reliance of continuity in the form of tensors.
I am proposing a complementary approach: more discrete and digital in nature. And, in some sense, strictly diophantine, relying on group theory and information science concepts heavily. However, it is important to still use the insights of conventional mathematics and physics of Einstein and Newton (cosmological and particle physics data measurements) but adding more recent discovered mathematics such as Non-Abelian finite simple groups and Moufang loops. In addition, information science models, as in Petri nets, Moore and Mealy machines, are used to add clarity to quantum processes at Planck scales.