Define a density plot?

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Asking for the doc via ?density_plot in the sage console gives a lot of information:

Signature:      density_plot(*args, **kwds)
Docstring:     
   "density_plot" takes a function of two variables, f(x,y) and plots
   the height of the function over the specified "xrange" and "yrange"
   as demonstrated below.

   "density_plot(f, (xmin,xmax), (ymin,ymax), ...)"

   INPUT:

   * "f" -- a function of two variables

   * "(xmin,xmax)" -- 2-tuple, the range of "x" values OR 3-tuple
     "(x,xmin,xmax)"

   * "(ymin,ymax)" -- 2-tuple, the range of "y" values OR 3-tuple
     "(y,ymin,ymax)"

   The following inputs must all be passed in as named parameters:

   * "plot_points" -- integer (default: 25); number of points to
     plot in each direction of the grid

   * "cmap" -- a colormap (default: "'gray'"), the name of a
     predefined colormap, a list of colors or an instance of a
     matplotlib Colormap. Type: "import matplotlib.cm;
     matplotlib.cm.datad.keys()" for available colormap names.

   * "interpolation" -- string (default: "'catrom'"), the
     interpolation method to use: "'bilinear'", "'bicubic'",
     "'spline16'", "'spline36'", "'quadric'", "'gaussian'", "'sinc'",
     "'bessel'", "'mitchell'", "'lanczos'", "'catrom'", "'hermite'",
     "'hanning'", "'hamming'", "'kaiser'"

   EXAMPLES:

and so on. (Truncated.) The many doc examples are not related to the option specifying the color map...

The one subquestion about the function (being a synonym to curve, or not), is immediately cleared, density plots are done for functions from a domain inside $\mathbb R^2$ with values in $\mathbb R$. The "height" of a function is then "giving the color".

(So the graph is not a curve in plane, but a "hill in 3D", the height is picking "the right color" from the color chosen scheme.)

The colors now.

From the sage interpreter console, the default seems to be "gray". The question mentions red + blue, so i have to guess that some other interface is using these colors by default. Possible color schemes are in the list:

sage: import matplotlib.cm
sage: cmapList = matplotlib.cm.datad.keys()
sage: cmapList . sort()
sage: cmapList[:10]
[u'Accent',
 u'Accent_r',
 u'Blues',
 u'Blues_r',
 u'BrBG',
 u'BrBG_r',
 u'BuGn',
 u'BuGn_r',
 u'BuPu',
 u'BuPu_r']

(Only the first ten shown.)

Starting from the code:

var( 'x,y' );
def f(x,y):    return exp( -x^2-y^2 )

one can thus try the color maps / schemes:

density_plot( f, (x,-1,1), (y,-1,1) )    # gray
density_plot( f, (x,-1,1), (y,-1,1), cmap='Accent' )
density_plot( f, (x,-1,1), (y,-1,1), cmap='Spectral' )
density_plot( f, (x,-1,1), (y,-1,1), cmap='Blues' )
density_plot( f, (x,-1,1), (y,-1,1), cmap='brg' )
density_plot( f, (x,-1,1), (y,-1,1), cmap='brg_r' )    # brg reversed
density_plot( f, (x,-1,1), (y,-1,1), cmap='gnuplot' )

and so on.