Wikimore

Description

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

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

The green stripe is caused by the plot being done at an insufficient resolution for the extremly (and infinitely) fine detail near 0.

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(Abs%20Imag%20Part%20at%20Infinity).png Category:PD-self#Exponential%20Function%20(Abs%20Imag%20Part%20at%20Infinity).png

MuPAD Code

  q := abs(Im(exp(1/(x+I*y)))):

  conts := 21:
  projectionlevel:=-10:
  ylimit := 1:
  xlimit := 1:
  submeshlevel := 30:

zmin := 0:
zmax := 10:
color := zip(RGB::Red, RGB::SapGreen,
             (a, b) -> (q(x,y)-zmin)/(zmax-zmin)*a
                      +(zmax-q(x,y))/(zmax-zmin)*b):

funcplot := plot::Function3d(q(x,y),
                             x = -xlimit..xlimit,
                             y = -ylimit..ylimit,
                             Mesh = [25, 25],
                             Submesh = [submeshlevel,submeshlevel],
                             LineColor = RGB::Black.[0.4],
                             LineWidth = 0.15,
                             FillColorFunction = color,
                             AxesTitleFont = ["Courier New", Bold, 14],
                             ViewingBoxZRange = -10..10
                            ):

contours := plot::modify(funcplot,
                         ZContours = [Automatic, conts],
                         LineWidth = 0.2,
                         LineColor = RGB::Gray90.[0.5],
                         XLinesVisible = FALSE,
                         YLinesVisible = FALSE,
                         Filled = FALSE
                        ):
                        
projcontours := plot::Transform3d([0, 0, projectionlevel],
                                  [1, 0, 0, 0, 1, 0, 0, 0, 0], 
                                   plot::modify(funcplot, ZContours = [Automatic, conts],
                                                LineWidth = 0.2,
                                                LineColorType = Dichromatic,
                                                LineColor = RGB::Red.[0.99],
                                                LineColor2 = RGB::Green.[0.99],
                                                XLinesVisible = FALSE,
                                                YLinesVisible = FALSE,
                                                Filled = FALSE
                                               )
                                  ):
                             
camera := plot::Camera([-20, -35, 300],
                       [0, 0, 0],
                       0.06
                      ):
                             
ploteverything := plot::Canvas(funcplot, contours, projcontours,
                               Width = 8.5*unit::inch, 
                               Height = 7*unit::inch,
                               camera
                               ): 
                          
plot(ploteverything)

Category:Surface plots of complex exponential function Category:Images with MuPad source code

Wikimore

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

MuPAD Code