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. > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
