Image:Essential singularity.png

From Wikipedia, the free encyclopedia

Wikimedia Commons logo This is a file from the Wikimedia Commons. The description on its description page there is shown below.
Commons is a freely licensed media file repository. You can help.
Description

Hue-luminance plot of exp(1/z), centered on the essential singularity at zero.
Source

self-made
Date
Author

Functor Salad
Permission
(Reusing this image)

see below

Visible domain: [-0.7,0.7]\times[-0.7,0.7]. The hue represents the complex argument; the luminance represents the absolute value. After some experimentation, I chose the following luminance mapping:

\operatorname{luminance}(z) = \operatorname{atan} (\ln (|z|^{0.6}))

This yields a value between -pi/2 and +pi/2, which was then affinely transformed into the required [0,1] range. I chose a slowly-growing function in order to avoid the hue getting drowned by black and white too much.

The resulting color map looks like this:

Visible domain: [-5,5] × [-5,5]
Visible domain: [-5,5] × [-5,5]


GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation license, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation license".

Aragonés | العربية | Asturianu | Български | বাংলা | ইমার ঠার/বিষ্ণুপ্রিয়া মণিপুরী | Brezhoneg | Bosanski | Català | Cebuano | Česky | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | فارسی | Suomi | Français | Gaeilge | Galego | עברית | Hrvatski | Magyar | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Kurdî / كوردی | Latina | Lëtzebuergesch | Lietuvių | Bahasa Melayu | Nnapulitano | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Occitan | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | తెలుగు | ไทย | Türkçe | Українська | اردو | Tiếng Việt | Volapük | Yorùbá | ‪中文(中国大陆)‬ | ‪中文(台灣)‬ | +/-

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeDimensionsUserComment
current18:52, 4 September 20072,000×2,000 (951 KB)Functor Salad ({{Information |Description=Hue-luminance plot of exp(1/z), centered on the essential singularity at zero. |Source=self-made |Date= |Author= Functor Salad }} Visible domain: <math>[-0.7,0.7]\times[-0.7,0.7]</math> The hue represents)
The following pages on the English Wikipedia link to this file (pages on other projects are not listed):