Wikimore

Description

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

z={\bigg |}\operatorname {Re} \left(\exp \left({\frac {1}{x+iy}}\right)\right){\bigg |}

The colour code is based on the arctan function and therefore emphasises changes at small values more than changes at large values. Green is smallest, then blue, red and yellow (largest).

Date

20 April 2007

Source

Own drawing, Plotted in MuPAD

Author

Inductiveload

Permission
(Reusing this file)

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.

Category:Self-published work#Exponential%20Function%20(AbsReal%20Part%20at%20Infinity)%20Density.png Category:PD-self#Exponential%20Function%20(AbsReal%20Part%20at%20Infinity)%20Density.png

MuPAD Code

f := abs(Re(exp(1/(x+I*y)))):

  ylimit := 1:
  xlimit := 1:
  mesh := 1600:
  
  hsv := (x, y, z) -> RGB::fromHSV([120+190*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):

Category:Complex color plots of exponential function Category:Images with MuPad source code

Wikimore

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

MuPAD Code