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When I plot a uniform field with zero values everywhere with the following command: VectorPlot[{y - y, x - x}, {x, -3, 3}, {y, -3, 3}] the result are horizontal arrows of considerable length.

I would expect to see nothing plotted, or infinitesimally small arrows.

That creates problems when I have a varying velocity field with time, where at some time instants the velocity is zero everywhere.

Is there a way to get around this problem?

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When I run VectorPlot[{y - y, x - x}, {x, -3, 3}, {y, -3, 3}] I get an empty plot. What version of Mathematica are you running? – David Slater Oct 9 '12 at 19:21
Thank you for your answer! I am using Mathematica 7. – stavros Oct 9 '12 at 19:22
@stavros You command gives me an empty plot in versions 7 and 8. – Mark McClure Oct 9 '12 at 19:42
I wish I could get the same result:) Anyway, thanks a lot for taking time to help me! – stavros Oct 9 '12 at 19:55
I also get an empty plot, using version 7. Have you tried restarting Mathematica completely? Are you loading any packages (Needs["package`"] or << package` ) on start-up? – Mr.Wizard Oct 9 '12 at 20:36
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