I'm trying to visualise the graph of a function $f(x,y)$ of two real variables using
ContourPlot. Here are the things I'm after:
The points where $f(x,y)=0$ should be easily seen. This can be done with a separate
ContourPlotof the form
There should be a clear distinction between the areas where $f(x,y)>0$ and $f(x,y)<0$. For example, the positive areas will coloured in shades of green, and the negative ones with shades of red.
The plot should be symmetric with respect to the contour line $f(x,y)=0$. That is, if we're using different shades of green and red say, the points where $f(x,y)=10$ should have the same brightness as those where $f(x,y)=-10$.
To give an example, I'm not satisfied with the default
since it's not easy to tell the positive and negative areas apart.
I would appreciate any help on this. Thanks!