# Mathematica VectorFieldPlot axes

• Mathematica
I have done some research and it seems like the option to add axes to VectorFieldPlot isn't available in my 6.0.0 version. (Unless someone knows how to do this?) Because of that, I'm having problems understanding how the axes limits command is working.

For the Plot command, even though it states that it should be entered {x, xmin, xmax} and {y, ymin, ymax}, it seems to automatically switch the xmin and xmax if they are entered backwards. Now, I am having trouble figuring out if VectorFieldPlot does something similar. When entered backwards {x, xmax, xmin} and {y, ymax, ymin} it doesn't seem to produce the expected "backwards" graph. What is even more confusing is that:
{x, xmax, xmin} and {y, ymax, ymin}
{x, xmax, xmin} and {y, ymin, ymax}
{x, xmin, xmax} and {y, ymax, ymin}
all produce the same graph.

Any one know whether or not it automatically plots the lowest limit on the left/bottom? Or how to explain the above behavior?

Thanks!

fresh_42
Mentor
I could imagine that the software determines automatically the appropriate limits. A possibility could be to integrate the axis into the object you want to plot, as part of the vector field.

Without a concrete example, I can't tell whether you are using asymmetric functions in your VectorFieldPlot or not. To determine whether VectorFieldPlot is reordering the plot ranges can you choose a function that is clearly asymmetric in both x and y and see by inspection whether it is doing this or not? Perhaps {2x,y^3} would be a field which should settle this.

To get axes added to VectorFieldPlot could you do something like this

Code:
Show[Plot[0,{x,1,3},PlotRange->{{1,3},{1,2}}],VectorFieldPlot[{2x,y^3},{x,1,3},{y,1,2}]]

which creates an empty plot with the appropriate range with axes and a vector field plot with the appropriate range without axes and then overlays those with Show.

Unfortunately I cannot test this under version 6 so I cannot verify whether this will work for you or not.

(Only after submitting this answer did I notice the original question was ten years old)

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