After some struggling I got my first plots with quiver working.
A simple plot is very simple, but a complicated one is very different.
Right now I have a 80x80 grid with multiple plots and I plan to go up. 
For this I need full control of the arrow dimensions.

The only way I can get narrow arrow is by setting width:
plt.quiver(x,y,u,v, width=0.001, headwidth=3, scale=0.07,...
works fine for me. But I would like to set the linewidth per arrow.

On stackoverflow I found:
widths = np.linspace(0, 2, X.size)
plt.quiver(X, Y, cos(deg), sin(deg), linewidths=widths)

This did not work for me: the minimum width was too large.
I there a way to create narrow arrows with varying width?

Thanks

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