Surfaces with Function Textures

p[r_,t_]:={Re[r^3*(Cos[t]+I*Sin[t])^3],
Im[r^3*(Cos[t]+I*Sin[t])^3],r*Cos[t]/3};
STPP[cm_,m_]:=ParametricPlot3D[p[r,t],{r,0,1},{t,0,4Pi},
PlotPoints->50,Mesh->None,Boxed->False,Axes->False,
ImageSize->400,ColorFunction->Function[{r,t},
ColorData[cm][Abs[r*Sin[m*t]]]]];
STPP["BrightBands",289]