Riemann Surface Transition

Manipulate[
ParametricPlot3D[Evaluate@{Re[(1-α)(r Exp[I φ])^2+α(r Exp[I φ])^3],
Im[(1-α)(r Exp[I φ])^2+α(r Exp[I φ])^3],r Cos[φ]},
{r,0, 2},{φ,-Pi,Pi}, PlotRange -> All, Mesh -> False, 
ColorFunction->(Hue[#5]&),PlotPoints -> ControlActive[{30,10},{60, 20}],MaxRecursion->1,BoxRatios->{1,1,1},PlotRange -> All,Axes->False,ImageSize->{435,435},Boxed->False,MaxRecursion->ControlActive[0,2]],
{{α,0,"%"},0,1}]

CAPTION

Transition between the Riemann surface of two sheets w(z)=(z^(1/2)) and the Riemann surface of three sheets w(z)=(z^(1/3)).

DETAILS

% — percentage of the Riemann surface of w(z)=(z^(1/3))

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Riemann Surface Transition" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/RiemannSurfaceTransition/

Contributed by: Michael Trott

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