Talk:Domain coloring

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Is it necessary to mention Riemann surfaces in this article at all? It seems that it has nothing to do with domain coloring. Maybe add a section on other methods of visualizing of complex functions? Lahvak 04:39, 17 April 2007 (UTC)[reply]

I corrected the unit circle image. Previously the legend for the phase of cyan said "2pi mod 2pi", which was incorrect. I changed it to "pi mod 2pi", which is correct tryptographer (talk) 04:01, 31 December 2007 (UTC)[reply]

Complex mapper link broken

External link to Complex Mapper and also author's link are broken. The new site seems to be this: http://alessandrorosa.altervista.org/ —Preceding unsigned comment added by 213.140.14.134 (talk) 10:29, 28 November 2008 (UTC)[reply]

self linking and other issues in /Using the third dimension to represent modulus/

I think that the section on /Using the third dimension to represent modulus/ is a self link, because the reference for it goes to User:Hansfbaier's blog here: http://www.hansfbaier.de/wordpress/computers-and-mathematics/ Self-linking aside, I think that 3d extensions to domain coloring are (or should be) beyond the scope of this article for the following reasons: one, most visualizations of domain coloring are expressly 2d, two, we're not talking about Kaehler manifolds here tryptographer Sat Sep 26 09:07:43 EDT 2009

the self-linked content has been deleted tryptographer (talk) 04:27, 29 June 2010 (UTC)[reply]

Consistency

I would like to propose, that across all the complex analysis pages featuring domain coloring, that we use <a href="http://code.google.com/p/mpmath/">mpmath</a> to generate the pictures for consistency's sake. tryptographer (talk) 04:01, 18 July 2010 (UTC)[reply]

Content/scope edit war?

There seems to be an bit of a war going about some content that would expand the scope of this article a bit, but no discussion here about it. It looks to me like a compromise would be in order, if the new material is sourced. I'd be happy to look at it, but don't want to chase it down across multiple user talk pages. Dicklyon (talk) 16:49, 11 April 2012 (UTC)[reply]

@Dicklyon, go ahead, do not care any more. Glenzo999 (talk) 15:47, 4 April 2013 (UTC)[reply]

The need for the merge seems obvious to me -- how could it be undesirable? Fgnievinski (talk) 03:05, 5 April 2013 (UTC)[reply]

MERGE

I have merged and remerged and reremerged this page. I am tired of this edit war. who ever is doing please stop... ;( Glenzo999 (talk) 16:17, 12 April 2012 (UTC)[reply]

Um, you're the one edit-warring over a merge that nobody wants - you've never given a reason why it's necessary. Why not explain yourself? MikeWazowski (talk) 17:24, 12 April 2012 (UTC)[reply]

Pictures

The pictures look nice, but for sin(x), why does the color change along the line im(z)=0? sin(x+0y) is real, so shouldnt it be red all along this horizontal line ? — Preceding unsigned comment added by 129.78.233.211 (talk) 03:32, 24 July 2013 (UTC)[reply]

sin(x) is real indeed for real x, but it can be either positive or negative depending on what x is, so the argument of the value varies between 0 (red) and

π

(cyan), except when sin(x)=0, which is where you see the black dots. Double sharp (talk) 04:19, 23 March 2016 (UTC)[reply]

First figure caption has an unreadable equation.

On my (firefox) browser, the equation in the first figure caption is clipped. The function is

ƒ(x) =(x² − 1)(x − 2 − i)²/(x² + 2 + 2i).

Perhaps you could put refer to this figure in the lede and use TEX format?

f(x)={\frac {(x^{2}-1)(x-2-i)^{2}}{x^{2}+2+2i}}

I know that adds length to the article. But nobody is saying that it is too long!--guyvan52 (talk) 16:18, 21 December 2014 (UTC)[reply]

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Mod for argument

I like the explanations next to the coloring diagram, except for one detail: Of course it is correct to consider the phase as a congruence class, but I don't think this concept is necessary to understand the article. Phase (waves) gets along fine without mod, and we all refer to time without saying something like "I get up at 8 a.m. mod 24". So we don't need to introduce mod for this topic. Are there any objections if I create an image without "mod 2π" removed for use in this article? — Sebastian 15:01, 18 December 2017 (UTC)[reply]

cplot

I've created cplot [1] for domain coloring with CAM16 in Python. Perhaps something for the references section?

[1] https://github.com/nschloe/cplot — Preceding unsigned comment added by Nschloe (talk • contribs) 19:19, 22 September 2018 (UTC)[reply]

Explaining an image

Hi,

In the first image, https://en.wikipedia.org/wiki/File:Domain_coloring_x2-1_x-2-i_x-2-i_d_x2%2B2%2B2i.xcf, there are white lines (for argument), black lines (for module), and then there are smaller lines, in the background. Can anyone state what they represent ? I believe it's missing in the article — Preceding unsigned comment added by Arthur MILCHIOR (talk • contribs) 14:18, August 7, 2019 (UTC)

The French description on the image explains it. Google Translate says: "The color (hue) represents the argument of the function. The black and white lines (saturation, value) represent the values of the constant modulus function. This file has 4 layers: the white lines indicating the iso-argument lines every pi / 6, the transformed grid of the complex plane, the intensity variations representing the module, the color representing the argument". I'm not an expert on this, but that seems like a correct explanation. --Pokechu22 (talk) 19:41, 7 August 2019 (UTC)[reply]

Color blindness references

I think the color-blindness claim is fairly obvious, but I haven't been able to find any perfect sources for it. The closest I found is "Visualizing modular forms" which says on the first page "While many of these are purely aesthetic, some offer color choices friendly to color blind viewers" (but only in v1^[1]; v2^[2] changes it to "others are chosen to allow the most accurate perception by as many viewers as possible"); as far as I can tell this hasn't been published yet. There's also "Domain Coloring and the Argument Principle"^[3] which says on page 4 "Before we go on, however, I should admit an obvious disadvantage of this technique: Not everyone sees color the same way" (but doesn't explicitly talk about colorblindness). A third mention (by the same author) in "Creating Symmetry: The Artful Mathematics of Wallpaper Patterns"^[4] says that "I have taught this material to students with limited color vision, and it seemed to work when they designed their own color wheels made from tones that they could easily distinguish." I'm not adding these references myself since I'm not sure how good they are, but I do think the information belongs in the article. (@Betseg for context) --Pokechu22 (talk) 21:23, 3 November 2020 (UTC)[reply]

References

^ Lowry-Duda, David (2020). "Visualizing modular forms". arXiv:2002.05234v1 [cs.GR].
^ Lowry-Duda, David (2020). "Visualizing modular forms". arXiv:2002.05234v2 [cs.GR].
^ Farris, Frank A. (2017). "Domain Coloring and the Argument Principle". PRIMUS. 27 (8–9): 827–844. doi:10.1080/10511970.2016.1234526. S2CID 126018409.
^ Farris, Frank A. (2 June 2015). Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. Princeton University Press. pp. 36–37. ISBN 978-0-691-16173-0.

[1] Lowry-Duda, David (2020). "Visualizing modular forms". arXiv:2002.05234v1 [cs.GR].

[2] Lowry-Duda, David (2020). "Visualizing modular forms". arXiv:2002.05234v2 [cs.GR].

[3] Farris, Frank A. (2017). "Domain Coloring and the Argument Principle". PRIMUS. 27 (8–9): 827–844. doi:10.1080/10511970.2016.1234526. S2CID 126018409.

[4] Farris, Frank A. (2 June 2015). Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. Princeton University Press. pp. 36–37. ISBN 978-0-691-16173-0.

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