Finding Surface for Complex ParametricPlot3D

  • Thread starter Thread starter zxh
  • Start date Start date
  • Tags Tags
    Complex Surface
Click For Summary
Complex plot visualization typically involves a 4D representation, making it challenging to intuitively color real and imaginary components. Using Mathematica's ParametricPlot3D can provide comprehensive information, although it often leaves the z-axis underutilized. The goal is to find a surface that, when projected onto the xy-plane, reveals iso displacement lines of the complex parametric plot. Alternative methods like computing grid line density for the z-value have been considered, but they yield different results than expected. The discussion raises questions about the connection to Riemann surfaces and the implications of higher values of k leading to self-intersecting projections.
zxh
Messages
8
Reaction score
0
Normally, complex plot visualization is a 4D problem. Coloring re or I am 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:
Physics news on Phys.org
nobody? is this graduate stuff?
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • Poll Poll
  • · Replies 1 ·
Replies
1
Views
5K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 18 ·
Replies
18
Views
6K
  • · Replies 21 ·
Replies
21
Views
8K
  • Poll Poll
  • · Replies 3 ·
Replies
3
Views
6K
  • · Replies 1 ·
Replies
1
Views
4K