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 Jo van Schalkwyk
Sent: Friday, April 14, 2017 6:18 AM
To: [email protected]
Subject: Re: [Jprogramming] Complex functions visualization
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.
>
>
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