For matching parameter values, where Loxodrome01 "Shift" corresponds to LogSpiral4 "Scale,"
the Loxodrome spiral is the inverse stereographic projection of the LogSpiral4 curve.
For Scale > 1, the planar log spiral expands, and the upper loxodrome shrinks toward the north pole.
Not sure how the bottom curve relates to the planar log spiral.

Loxodrome Sweep of a circle:

- Brian