AnglePath Rotations 2

APG2[m_,s_,c_]:=Module[{coef,col},
coef=RandomInteger[{2,100}]; col=RandomReal[{0,1}];
path[a_]:=Graphics[{Opacity[.3],Hue[col],
Rotate[Line[AnglePath[N[Log[coef]*Range[-1000,1000]]]],a]}];
Show[Table[path[i*Pi/m],{i,2m}],

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

APG2[7,500,"slategray"]

{APG2[4,300,"black"],APG2[11,300,"ghostwhite"]}