  This article is the second in a series of two presenting the Scale
Relativistic approach to non-differentiability in mechanics and its relation to
quantum mechanics. Here, we show Schroedinger's equation to be a reformulation
of Newton's fundamental relation of dynamics as generalized to
non-differentiable geometries in the first paper \cite{paper1}. It motivates an
alternative interpretation of the other axioms of standard quantum mechanics in
a coherent picture. This exercise validates the Scale Relativistic approach
and, at the same time, it allows to identify macroscopic chaotic systems
considered at time scales exceeding their horizon of predictability as
candidates in which to search for quantum-like structuring or behavior.
