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File:Exponential Function (Imag Part) Density.png

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Original file (850 × 700 pixels, file size: 40 KB, MIME type: image/png)

Description
English: Diagram of the real part of exponetial function in the complex plane. The density is given by:
Blue represents high values, red represents low values. Please note that the colouring is non-linear (it is based on the ArcTan function, see the code below), and therefore a similar change in hue does NOT necessarily denote a similar change in value.
Date
Source Own drawing, Plotted in MuPAD
Author Inductiveload
Permission
(Reusing this file)
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

MuPAD Code


  f := Im(exp(x+I*y)):

  ylimit := 2*PI:
  xlimit := 3:
  
  hsv := (x, y, z) -> RGB::fromHSV([121+85*arctan(z), 1, 1]):
  
  cplot := plot::Density(f, 
                         x = -xlimit..xlimit, 
                         y = -ylimit..ylimit, 
                         Mesh = [800, 800],
                         AxesTitleFont = ["Courier New", Bold, 14],
                         TicksLabelFont = ["Arial", 10],
                         FillColorFunction = hsv,
                         YTicksNumber = None,
                         YTicksAt = [-3*PI/2 = "-3 PI/2", -PI = "-PI", -PI/2 = "-PI/2", -2*PI = "-2 PI",
                                     0 = "0", 
                                     PI/2 = "PI/2", PI = "PI",  3*PI/2 = "3 PI/2", 2*PI = "2 PI"],
                         XTicksDistance = 0.5):
  
  plot(cplot,
       Axes = Frame,
       Width = 8.5*unit::inch, 
       Height = 7*unit::inch):

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20 April 2007

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Date/TimeThumbnailDimensionsUserComment
current23:57, 20 April 2007Thumbnail for version as of 23:57, 20 April 2007850 × 700 (40 KB)Inductiveload
15:26, 20 April 2007Thumbnail for version as of 15:26, 20 April 2007850 × 700 (105 KB)Inductiveload{{Information |Description=Diagram of the real part of exponetial function in the complex plane. The density is given by: ::<math>z=\operatorname{Re} \left (\exp \left( x + i y \right)\right)</math> Blue represents high values, red represents low values.

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