plot::Conformal – (complex-valued) conformal function plot

plot::Conformal(f(z), z = ) is a plot of the conformal function over the complex interval .

Call:

plot::Conformal(f, z = z1 .. z2, <a = amin .. amax>, Options)

Parameters:

f:	An expression in z and the animation parameter, if present. Expected to be conformal in z. f is equivalent to the attribute Function.
z:	The independent variable: An identifier or indexed identifier. z is equivalent to the attribute ZName.
z1 .. z2:	The (complex) range over which f should be plotted: z1 and z2 should be complex-valued expressions, possibly in the animation parameter. z1 .. z2 is equivalent to the attribute ZRange.

Details:

plot::Conformal creates plots of (conformal) complex-valued functions of one complex variable. They are displayed by showing the image of a rectangular grid over an interval.
By default, the attribute LineColorType = Flat is set. All curves are displayed with the color given by the attribute LineColor (or Color for short).

When specifying the attribute LineColorType = Dichromatic, a color blend from LineColor to LineColor2 is used (“height coloring”).

When specifying the attribute LineColorType = Functional without specifying a LineColorFunction, all curves parametrized by the real part of the pre-image points are displayed with the flat color LineColor, whereas all curves parametrized by the imaginary part of the pre-image points are displayed with the flat color LineColor2.

A user defined LineColorFunction is a procedure (z, x, y, flag) -> RGB-color that will be called with complex floating point arguments z from the range of pre-images of the conformal function f, the real floating point values x = Re(f(z)), y = Im(f(z)), and the integer value flag which has the values 1 or 2. The flag value determines the color of the curves parametrized by the real part of z, the flag value determines the color of the curves parametrized by the imaginary part of z. The color function must return an RGB color, i.e., a list of 3 real floating point values between and . For example,

     LineColorFunction = proc(z, x, y, flag)
     begin
       if flag = 1 then
          return(RGB::Blue)
       else
          return(RGB::Red)
       end_if;
     end_proc



displays all curves parametrized by Re(z) in blue, while the orthogonal curves, parametrized by Im(z), are displayed in red.
See the examples in the documentation of RGB for another way of displaying complex functions.