ϕ[s_]:=2+Cos[s];ψ[s_]:=Sin[s];DynamicModule[{cols},cols=RGBColor/@{"#A64942","#FF7844","#FFAB5E","#23425F"};Manipulate[ParametricPlot3D[Table[{iϕ[v]Cos[u],ϕ[v]Sin[u],ψ[v]}/.{u->ArcSin[yp/(2+Cos[v])]},{yp,3-y,-3,-3/8},{i,{-1,1}}],{v,0,2π},Boxed->False,Axes->None,PlotStyle->Table[Directive[Thickness[.004],Blend[Reverse[cols[[;;3]]],(y+3/8i)/6]],{i,0,15}],PlotRange->{{-3.5,3.5},{-3.5,3.5},{-1.1,1.1}},ViewPoint->{0,0,2},ViewAngle->π/6,PlotPoints->200,ImageSize->540,Background->cols[[4]]],{y,0,3/8}]]