It is shown in the present work that the distorted-space model of matter as extended to mimics of the proton and neutron can be described as muonic-based structures. These distorted-geometry structures exhibit non-Newtonian features wherein the hole or core-region fields of the structure (negative pressure core for a positive-charge positive-pressure large-r structure) do not behave functionally in a r−4 manner and terminate at zero at the radial origin (no singularity). Of particular interest is that of r−6 energy-density behavior at structural radial distances near the core of the distortion, a region also displaying potential-well behavior.