# Animated Vector plot

I'm trying to make an animation of a time-varying 2D vector field. However, I'm got a difficulty in that Mathematica normalises the length of the vectors with each call to VectorPlot.

A (very simple) example:

myField = {Cos[2 π t], 0};

Animate[
VectorPlot[myField /. t -> TT, {x, -1, 1}, {y, -1, 1}],
{TT, 0, 1}]


Expected result: The arrows grow and shrink in time

The actual result: The arrows remain the same size, but flick direction

Is there some way to fix the length of the arrows relative to the field value?

• You've seen VectorScale? – J. M.'s ennui Jun 11 '13 at 13:35

As @Ox4A4D mentioned in the comment, you could use the option VectorScale to set the length of vectors, here is an example code:

myField = {Cos[2 \[Pi] t], 0};
Animate[VectorPlot[myField /. t -> TT, {x, -1, 1}, {y, -1, 1},
VectorScale -> Abs[0.05 Cos[2 Pi TT]]], {TT, 0, 1}]

• Ah, I see -- it's making use of the fact that you know what the maximum value is with this simple function. Perhaps that will put me on the right track... – Gremlin Jun 11 '13 at 15:04

With a slightly more interesting function, and cleaner syntax:

myField[x_, y_, t_] := {Cos[2 Pi x t], Sin[2 Pi y t]};

Animate[VectorPlot[myField[x, y, t], {x, -1, 1}, {y, -1, 1},
VectorScale -> {Small, 1, None}], {t, 0, 1}]


Check the documentation and play around with the arguments to VectorScale as required.

EDIT:

I had indeed misunderstood your requirements. mm.Jang's answer is what you're looking for. 0.05*Norm[myField[t]] should generalize it.

• Your code somehow doesn't work for me... I'm using MMA 9.0.1.0 by the way... – Rod Jun 11 '13 at 13:53
• Any error? I'm on 9.0.0.0 on 64-bit Linux. – Corey Kelly Jun 11 '13 at 13:59
• @RodLm you must run Clear[myField]; first. – mmjang Jun 11 '13 at 14:00
• @CoreyKelly Yes, when I run your code nothing happens. I mean, the slider t moves itself but no vector plot is shown. – Rod Jun 11 '13 at 14:00
• @mm.Jang Thank you... problem solved! Corey, please forget what I've written before. – Rod Jun 11 '13 at 14:02