Christian Froeschlin <chr### [at] chrfrde> wrote:
> It should be noted that while povray can make nice renderings of
> the geometry, this is not necessarily related to what a typical plot
> looks like (that may be intended to convey information about the
> structure using contour lines, wireframes and such). Such elements
> do not come naturally in the render process and would need to be
> constructed as additional geometry.
>
Although this is true for an arbitrary mesh, when rendering a function it's
often possible to map the function (or its inverse) to a repeating pattern and
use that as a texture.

In this case, another, simpler alternative is to simply extrude a polar graph
paper pattern.  Applying the layered texture below results in a render similar
to the illustration, with black radial and circumferential lines, though it has
a solid base color.  (Radial gradients applied to each branch so the colors
match at the ends could also be used.)

#include "colors.inc"
....
  texture{ pigment{
    radial frequency 10 triangle_wave
    color_map{
      [0 Black][0.02 Black]
      [0.02 Violet+<0,0,0,0.85>]
      [0.98 Violet+<0,0,0,0.85>]
      [0.98 Black][1 Black]}
    rotate 90*x
    }
    finish{ specular 0.5 phong 0.5}
  }//end texture
  texture{ pigment{
    wood scale 0.2 triangle_wave
    color_map{
      [0 Black][0.04 Black]
      [0.04 Clear] [0.96 Clear]
      [0.96 Black][1 Black]}
    }
    finish{ specular 0.5 phong 0.5}
  }//end texture
....

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