Two comments and a question arising from the visualizations of the unit p-sphere in the plane....
Comment 1: Curiously, the built-in function Norm in its two argument form Norm[vec, p] prohibits values of p that are less than 1. Of course one may define a generalization:
norm[p_][x_List] := Total[Abs[x]^p]^(1/p)
Comment 2: It would be desirable to include all code!
Question: What exactly are you doing in the form of the visualization that uses complex numbers?
