File:Exponential Function (Imag Part at Infinity) Density.png

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Original file ‎(850 × 700 pixels, file size: 109 KB, MIME type: image/png)

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Description

Diagram of the value of imaginary part of exponential function in the complex plane, as the operand approaches infinity. The plot is given by:

The colour code is based on the arctan function and therefore emphasises changes at small values more than changes at large values. Red is smallest, blue is largest. Green is zero.
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[edit]

f := Re(exp(1/(x+I*y))):

  ylimit := 1:
  xlimit := 1:
  mesh := 1600:
  
  hsv := (x, y, z) -> RGB::fromHSV([121+85*arctan(z), 1, 1]):
  
  cplot := plot::Density(f, 
                         x = -xlimit..xlimit, 
                         y = -ylimit..ylimit, 
                         AntiAliased = TRUE,
                         Mesh = [mesh, mesh],
                         AxesTitleFont = ["Courier New", Bold, 14],
                         TicksLabelFont = ["Arial", 10],
                         FillColorFunction = hsv,
                         YTicksDistance = 0.5,
                         XTicksDistance = 0.5):
  
  plot(cplot,
       Axes = Frame,
       Width = 8.5*unit::inch, 
       Height = 7*unit::inch):

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Date/TimeThumbnailDimensionsUserComment
current02:34, 22 April 2007Thumbnail for version as of 02:34, 22 April 2007850 × 700 (109 KB)Inductiveload (talk | contribs){{Information |Description=Diagram of the value of imaginary part of exponential function in the complex plane, as the operand approaches infinity. The plot is given by: ::<math>z=\bigg|\operatorname{Re} \left (\exp \left( \frac{1}{x + i y} \right)\right)

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