Consider drawing the complex plane such that 1 is upwards and i is to the
right. Then complex conjugation correspond to left-right symmetry, which is
more familiar than up-down symmetry.
Bo.
Den 17:57 tirsdag den 11. april 2017 skrev Roger Hui
<[email protected]>:
V. cool.
On Tue, Apr 11, 2017 at 8:39 AM, Andrew Nikitin <[email protected]> wrote:
> I read a book "Visual Complex Functions" by Elias Wegert.
>
> In it autor argues for so called phase portraits as a good way to visualize
> complex function of one complex variable. Each function value is
> represented by
> a pixel with a hue (which is an angular quantity) equal to function value's
> phase angle. He argues that the result provides a lot of information about
> function and even allows to restore analytic functions (up to a constant).
>
> The other 2 components of the colorspace, saturation and light, can be
> used to show lines of equal phase and equal magnitude. Author calls it
> "enhanced phase portrait". Interesting, that there is no level tracing.
> Lines appear as a byproduct of using a modified hue palette.
>
> I put up a script and couple of sample images on wiki. 'sq' utility
> generates
> unit square of complex numbers. Evaluate your choice of function on it and
> color each pixel with ccEnhPh and you have yourself a phase portrait to
> view
> with viewmat or save with writebmp.
>
> http://code.jsoftware.com/wiki/User:Andrew_Nikitin/Phase_portraits
>
> I think that if you like pretty pictures (and want to get some insight on
> complex function behavior), this technique provides a lot of bang for a
> very
> little buck.
>
>
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