Finding Surface for Complex ParametricPlot3D

In summary, the conversation is about finding a surface that can accurately represent complex parametric plots and their iso displacement lines. The use of Mathematica's ParametricPlot3d is suggested as a potential solution, but there is also discussion about using density and contour plots. The connection to Riemann surfaces is mentioned, and there is speculation about the complexity of the problem and its relevance to graduate level studies.
  • #1
zxh
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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.
 
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  • #2
nobody? is this graduate stuff?
 

1. What is a parametric plot in 3D?

A parametric plot in 3D is a type of graph that displays the relationship between three variables, typically represented by x, y, and z coordinates. Unlike traditional 2D graphs, a parametric plot in 3D allows for the plotting of complex mathematical functions with multiple independent variables.

2. How do I find the surface for a complex parametric plot in 3D?

To find the surface for a complex parametric plot in 3D, you can use software or programming languages such as Mathematica, MATLAB, or Python. These programs have built-in functions and tools specifically designed for creating and visualizing complex parametric surfaces.

3. What are the challenges of finding the surface for a complex parametric plot in 3D?

The main challenge of finding the surface for a complex parametric plot in 3D is dealing with the large amount of data and calculations involved. Since parametric plots involve multiple variables and complex mathematical functions, it can be difficult to accurately plot and visualize the entire surface without specialized tools or software.

4. Can I manipulate the surface of a complex parametric plot in 3D?

Yes, depending on the software or programming language you are using, you can manipulate the surface of a complex parametric plot in 3D. For example, in Mathematica, you can use the Manipulate function to change the parameters and observe how it affects the surface of the plot.

5. Are there any real-world applications for complex parametric plots in 3D?

Yes, there are many real-world applications for complex parametric plots in 3D, particularly in fields such as physics, engineering, and computer graphics. For example, complex surfaces and shapes can be accurately modeled and visualized using parametric plots, allowing for better understanding and analysis of real-world phenomena.

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