Vector field using gnuplot

It seems this question/answer is a bit old, and since I believe that gnuplot is changed a bit in the latest versions, probably the answer should be updated.

I found a nice and compact solution here, by thse: http://gnuplot.10905.n7.nabble.com/Vector-Fields-td3627.html

which I will report for convenience:

set xrange [-5:5]
set yrange [-5:5]
# only integer x-cordinates
set samples 11
# only integer y-cordinates
set isosamples 11
# we need data, so we use the special filename "++", which
# produces x,y-pairs
plot "++" using 1:2:1:(2.*$2) with vectors

Here, the original question was how to plot the vector field F(x,y) = <x, 2y>. The trick is in the plot "++", which is a special file name which allows to use functions in the using specifier.

So, as @Jan said in his answer, gnuplot needs 4 fields in the data file to plot a vector field, but here the fields are synthetic and produced with two functions.

An equivalent formulation using defined functions could be:

set xrange [-5:5]
set yrange [-5:5]
dx(x) = x
dy(x) = 2*x
plot "++" using 1:2:(dx($1)):(dy($2)) w vec

See help special-filenames for further details.

HIH

As far as I can tell, gnuplot can only plot vector fields when reading data from a file. Your file will have to have 4 columns, x, y, deltax and delta y, and gnuplot will then plot a vector from (x,y) to (x+deltax, y+deltay) for each line in the file:

plot "file.dat" using 1:2:3:4 with vectors head filled lt 2

If you are not insisting on using gnuplot, there are other tools that can to this better or at least easier. I personally use asymptote. There is an example of a vectorfield plotted in asymptote here.