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In WolframAlpha we can easily visualize Riemann surfaces of arbitrary functions,

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can we plot the Riemann surface of an arbitrary function using Mathematica and with a better color scheme like these plots so that I can see the connection of the branches?

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Edit

Here are more Riemann surfaces by Matthias Nieser et. Automatic Generation of Riemann Surface Meshes

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related:

How can I recreate Trott's Riemann Surface plot in Mathematica?

Visualization of Riemann Surfaces of Algebraic Functions

Automatic Generation of Riemann Surface Meshes

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Perhaps should mention How can I recreate Trott's Riemann Surface plot in Mathematica? –  Artes Sep 8 '13 at 17:40
    
@Artes That's where confuses me. Does this kind of visualization of the Riemann surface in 3D is called "Trott's Riemann surface plot", or this color scheme is brought up by Trott? There are lots this kind of plot in the wiki page of Riemann surface, but none of them referred to "Trott". Also matlab has a function cplxmap that can plot this kind of 3d Riemann surface, and it doesn't mention "Trott" either. –  xslittlegrass Sep 8 '13 at 17:57
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Take a look at the first sentence in the question from the link Artes provided. –  Kuba Sep 8 '13 at 18:03
    
These are one of a number of ways to depict a Riemann surface. Another way, in my Application, is to use a multifunction capability and show a Riemann plane and using a Locator point with an attached arrow representing the complex value at that point. Dragging around the locator allows one to explore all parts of the surface in a smooth, single valued, continuous manner (just as Riemann claimed). With the Sqrt function you have to circle the origin twice to get back to the same point. You would have to contact me by email for more information. –  David Park Sep 8 '13 at 19:15

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