# Animated basic Vector plot

what codes are needed to properly animate a vector plot? this for example: VectorPlot[{y, -x}, {x, -3, 3}, {y, -3, 3}]. because i tried everything, i have read the help manual, and searched in youtube tutorials but i couldn't do it.

• What do you mean with animate? What do you want to animate? The vector field you gave is static the only thing there you could animate would be plot parameters or the field itself. Mathematica has the Animate and Manipulate function for this. – N0va Aug 30 '16 at 21:48
• My teacher just told us to make a vector field 2D and 3D to move ("animate"), but i have never used mathematica before. – Arturo Aug 30 '16 at 21:50
• Look at the Documentation for Animate and put in your vector plot instead of the normal plot from the example. Then you just need to chose what quantity you want to animate. The field itself could be one option: Animate[VectorPlot[{y, u*x}, {x, -3, 3}, {y, -3, 3}], {u, -2, 2}] – N0va Aug 30 '16 at 21:56
• thanks really, yes thats exactly what i didn't know how to do it. – Arturo Aug 30 '16 at 22:00
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Here is one possibility:

Clear[dx, dy, f, points, fmap, stages, stuff]

dx[x_, y_] := -9 y + (3 x^2 y)/4;
dy[x_, y_] := -9 x + x^3/4;
Clear[f]
f[{x_, y_}] := {0, 0} /; \[Not] (-10 <= x <= 10.1);
f[{x_, y_}] := {0, 0} /; \[Not] (-10 <= y <= 10.1);
f[{x_, y_}] := {x + .001 dx[x, y] , y + .001 dy[x, y]};

points = Partition[Table[RandomReal[{-4, 4}], 200], 2, 1]~Join~
Partition[Table[RandomReal[{-10, 10}], 200], 2, 1];

Clear[fmap];
fmap[{stuff___}] := f /@ {stuff};
stages = NestList[fmap, points, 100];
stages = stages /. {x_Real, y_Real} /; \[Not](-10 < x < 10) :>{0,0};

stuff = Show[StreamPlot[{-9 y + (3 x^2 y)/4, -9 x + x^3/4}, {x, -10, 10}, {y, -10, 10},
PlotTheme -> "Minimal"],
Graphics@{Red, PointSize[.015], Point[stages[[hh]]]},
PlotRange -> {{-10, 10}, {-10, 10}}
, Axes -> True]~Table~{hh, 1, 100, 1};

ListAnimate[stuff]  idea2

 Manipulate[
VectorPlot[{y - p[], x + p[]}, {x, -3, 3}, {y, -3, 3}],
{{p, {0, 0}}, Locator}]

Clear[dx, dy, f, points, fmap, stages, stuff]

dx[x_, y_] := y^3 - 9 x ;
dy[x_, y_] := x^3 - 9 y ;

f[{x_, y_}] := {0, 0} /; \[Not] (-10 <= x <= 10.1);
f[{x_, y_}] := {0, 0} /; \[Not] (-10 <= y <= 10.1);
f[{x_, y_}] := {x + .001 dx[x, y], y + .001 dy[x, y]};

points = Partition[Table[RandomReal[{-4, 4}], 200], 2, 1]~Join~
Partition[Table[RandomReal[{-10, 10}], 200], 2, 1];

fmap[{stuff___}] := f /@ {stuff};
stages = NestList[fmap, points, 100];
stages = stages /.{x_Real, y_Real} /; \[Not] (-10 < x < 10) :> {0,0};

stuff = Show[
StreamPlot[
{    y^3 - 9 x   ,     x^3 - 9 y  },
{x, -10, 10},
{y, -10, 10},
PlotTheme -> "Minimal"
],
Graphics@{Red, PointSize[.015], Point[stages[[hh]]]},
PlotRange -> {{-10, 10}, {-10, 10}},
Axes -> True
]~Table~{hh, 1, 100, 1};

ListAnimate[stuff]

• maybe change the points to vectors will have a better visual effect :) very impressive! +1 – Wjx Aug 30 '16 at 23:42
• good idea! I will try to do that. @Wjx – Conor Cosnett Aug 31 '16 at 20:38
• Also, you can ramdomly generate points in the animation process, so the dynamic can keep going. – Wjx Aug 31 '16 at 22:20
• falstad.com/vector probably the best simulation on the internet – Conor Cosnett Aug 15 '19 at 17:21
• another nice javascript simulation anvaka.github.io/fieldplay – Conor Cosnett Aug 15 '19 at 22:21