Hi All I think there's room for further improvement of your colorization of the images. Years down the line I still think the approach taken with PRAVDAcolor makes a lot of sense. Check out:
https://www.research.ibm.com/people/l/lloydt/color/color.HTM Bergman's paper is here: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.452.1807&rep=rep1&type=pdf Is this of any value to you? My 2c, Jo. On 14 April 2017 at 17:27, Linda A Alvord <[email protected]> wrote: > Andrew, These are fascinating images. > > Several years ago I tried to convince people that GRB would be a better > palette than RGB. I used Cliff's image, your first pattern, and rotated it > 90 degrees. If you think of this as the face of a clock, then in an hour > the GRB palette goes from white to black in a continuous value from light > to dark when seen as a grayscale. Green ns brighter than Red, which is > brighter than blue. > > require 'viewmat' > at2=: 13 :'([:{:"1 *.) j./"1 y' > RGB=: 255* #:i.8 > GRB=:1 0 2{"1 RGB > we=: 13 :'<.0++/"1[0.3 0.59 0.11*"1 y' > gray=: 13 :'3#"0 we y' > RGB viewmat (D=.at2"0 /~ i:500) > GRB viewmat (D=.at2"0 /~ i:500) > (gray RGB) viewmat (D=.at2"0 /~ i:500) > (gray GRB) viewmat (D=.at2"0 /~ i:500) > > (Another little exercise for JHS) > > Maybe you'll make some interesting discoveries with your other patterns. > > Linda > > -----Original Message----- > From: Programming [mailto:[email protected]] On > Behalf Of Andrew Nikitin > Sent: Tuesday, April 11, 2017 11:39 AM > To: J programming > Subject: [Jprogramming] Complex functions visualization > > 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 > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
