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

DescriptionExponential Function (Imag Part at Infinity).png	Diagram of the imaginary part of exponetial function in the complex plane, as the operand approaches infinity. The plot is given by: ${\displaystyle z=\operatorname {Im} \left(\exp \left({\frac {1}{x+iy}}\right)\right)}$ The countour lines correspond to integer heights, and the gridlines have spacings of 0.08.
Date	20 April 2007
Source	Own drawing, Plotted in MuPAD
Author	Inductiveload
Permission (Reusing this file)	Public domainPublic domainfalsefalse 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.

  q := Im(exp(1/(x+I*y))):

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

zmin := -10:
zmax := 10:
color := zip(RGB::Yellow, RGB::DarkGreen,
             (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::Yellow.[0.99],
                                                LineColor2 = RGB::DarkGreen.[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)