# Editing the graph to become with animation

In the following code:

p1=ParametricPlot3D[{ (3 + Cos[v]) Sin[u], (3 + Cos[v]) Cos[u], Sin[v]}, {u, 0, 2 Pi}, {v, 0, 2 Pi}]

p2=ParametricPlot3D[{Cos[Sqrt t](3 + Cos[t]), Sin[Sqrt t] (3 + Cos[t]), Sin[t]}, {t, 0, 50}]

p3=ParametricPlot3D[{Cos[Sqrt t](2 + Cos[t]), Sin[Sqrt t] (2 + Cos[t]), 8+Sin[t]}, {t, 0, 50}] /. Line -> ({CapForm[None], FaceForm[Green, White], Tube[#, .25]} &)

Show[p1,p2,p3] 1. How can I animate p2 and p3 to generate simultaneously?
2. How can I download the resulting animated graph as a video?
3. How can I remove the coordinates?

Thanks!

• For the last part, use Axes ->False.
– kglr
Jun 16 '19 at 7:17

p1 = ParametricPlot3D[{(3 + Cos[v]) Sin[u], (3 + Cos[v]) Cos[u],
Sin[v]}, {u, 0, 2 Pi}, {v, 0, 2 Pi},
PlotStyle -> Opacity[.5], Mesh -> None];

ClearAll[p2, p3]
p2[tmax_] := ParametricPlot3D[{Cos[Sqrt t] (3 + Cos[t]),
Sin[Sqrt t] (3 + Cos[t]), Sin[t]}, {t, 0, tmax}, PlotStyle -> Thick];
p3[tmax_] := ParametricPlot3D[{Cos[Sqrt t] (2 + Cos[t]),
Sin[Sqrt t] (2 + Cos[t]), 8 + Sin[t]}, {t, 0, tmax}] /.
Line -> ({CapForm[None], FaceForm[Green, White], Tube[#, .25]} &);

Manipulate[Show[p1, p2[tmax], p3[tmax], PlotRange -> All, Axes -> False], {tmax, 1, 50}] To export as a GIF animation:

frames = Table[Show[p1, p2[tmax], p3[tmax], PlotRange -> All], {tmax, 1, 50}];
Export["frames.gif", frames] • Can you please attach the animation here? I am using an online version of mathematica and it is not very good. Thanks always! Jun 16 '19 at 7:44