Helicoid=ParametricPlot3D[{t*Cos[v],t*Sin[v],2*v},{t,-10,10},{v,0,3*Pi},Background->Black, Boxed->False,Axes->False,Mesh->{20,40}]

HelicoidAnimated=Animate[Show[Helicoid,ParametricPlot3D[{t*Cos[v],t*Sin[v],2*v},{t,-10,10},Background->Black, Boxed->False,Axes->False,PlotStyle->{Red,Thick}]],{v,0,3*Pi,0.0001},DefaultDuration->10]