# Independent scaling of arrowheads and vectors in vector plot

I'd like to scale with independent parameters the vectors and the corresponding arrowheads in a vector plot. The basic code is as follows:

vecP = 9;
disk = 1.4;
vecScale = .1;
arrScale = .8;
thickn = 0.007;

toPlot[x, y]:=(4 E^(2 Im[ArcTan[x, y]] + 2 Re[-x^2 - y^2]) Abs[x^2 + y^2])/\[Pi];

vpm1 = VectorPlot[
toPlot[x, y] {y, -x}, {x, y} \[Element] Disk[{0, 0}, disk],
VectorPoints -> vecP,
VectorScale -> {vecScale, arrScale},
VectorStyle -> {Black, Thickness[thickn]},
]


Of course the above code doesn't work, as the "arrScale" parameter assigns a fixed dimension to each arrowhead in the plot (while vecScale is actually scaling the vectors).

What I'd like to do is to scale the arrowheads as well, but with a different scaling coefficient respect to the vector scaling.

I thought of doing something like:

VectorScale -> {vecScale, arrScale * #&}


as one would do in a ColorFunction approach:

ColorFunction -> (Blend[{White,Black}, #] &)


where the slot #& is referred to the plotted function's value point by point. However, this approach doesn't work in my specific case (if someone can explain me why I'd be glad :) ).

• Possible duplicate: mathematica.stackexchange.com/q/788/12 – Szabolcs Oct 10 at 7:33
• @Szabolcs thx for the link, I came across it before posting but I don't think it answer my question. I'm not 100% sure, but I think scaling the arrows in a Graphic (as in the link) or in a VectorPlot. Also, that post is very old and things might have changed in the meanwhile! – Fraccalo Oct 10 at 7:40
• Things didn't change regarding the link I gave, but you are right: I misread your question. The link is not relevant. (Just to be clear, I did not vote to close as duplicate, I merely gave the link.) – Szabolcs Oct 10 at 8:17
• @Szabolcs I really appreciate the community job here (therefore I don't get it personal even if someone votes to close my posts, I think it's perfectly normal and it might happen to everyone to post a duplicate!) and I embrace the "Possible duplicate" links as useful suggestions rather than personal critiques, so really no hard feelings :D – Fraccalo Oct 10 at 8:28

VectorPlot[toPlot[x, y] {y, -x}, {x, y} \[Element] Disk[{0, 0}, disk],