Optimistically, multifractal analysis might already be a sufficient tool, but that is just grasping in the dark. If I remember correct though, Nottale has a theory which sounds somewhat similar to the "all structure is emergent" idea called scale relativity (or something like that). Moreover, I would naively like to presume that maybe something simple but alternative like fractional calculus or multiplicative calculus may perhaps be useful alternative forms of calculus which might be enlightening w.r.t. naturally capturing or identifying the correct physical quantities or equations involved in such a framework. Else, perhaps more advanced algebraic-geometric or holomorphic notions would probably be necessary.