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Finding Surface for Complex ParametricPlot3D

  1. Sep 8, 2012 #1

    zxh

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    Normally, complex plot visualization is a 4D problem. Coloring re or im separately isn't very intuitive.

    Otoh, using Mathematica's ParametricPlot3d gives all the information and leaves us with the z-axis unused. Example for z→z+k/z:

    Yudkowski.jpg

    I'm trying to find a surface which when projected onto the xy-plane gives the iso displacement lines of the complex parametric plot. (Mathematica uses polygons for computation here).

    An alternative would be to compute the grid line density for the z-value.
    I looked at a density/contour plot, but it appears quite different:

    image.jpg

    How would you go about this? Is this connected to riemann surfaces? It seems for higher k's the surface would intersect/overlap itself/ project non-injective.
     
    Last edited: Sep 8, 2012
  2. jcsd
  3. Sep 10, 2012 #2

    zxh

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    nobody? is this graduate stuff?
     
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