AnglePath Rotations

APG[n_,m_,s_,c_]:=Module[{coef,col,f},
coef=RandomInteger[{1,100}]; col=RandomReal[{0,1}];
f=n*(E+.001coef+.1Sin[coef]);
path[a_]:=Graphics[{Opacity[.3],Hue[col],
Rotate[Line[AnglePath[N[f*Range[-100,700]]]],a]}];
Show[Table[path[i*Pi/m],{i,2m}],

ImageSize->s,Background->RGBColor[c]]]

{APG[32,8,300,"ghostwhite"],APG[128,11,300,"black"]}

APG[89,6,500,"slategray"]