Pepe,
Thank you very much for your links. I am color defective (red-green) so I
have never attended to colors much, though I find them quite fascinating.
To give you an idea, I have no idea what the colors magenta and cyan are,
but my spouse is helping me with it all. Anyhow the color wheel and its
sequence are foreign to me so I have to really study the graphics.
I gather that the imaginary component of a complex number is associated
with angles (measure in radians perhaps), which is very hard to understand.
So are these graphs like graphs of polar coordinates (which I never could
internalize, either)? What sense does that make?
I have been playing with Andrew's jwiki link and now understand more about
the graphs.
I have still not understood how (_2 3 _4^-)s etc produce straight lines of
finite length. What values of s are used and is the result the argument for
either zeta or eta functions so that it's the zeta or eta function that
produces the straight line, maybe?
I was disappointed that I could not play more with Andrews functions
because I get the following error, as well.
viewrgb 8 ccEnhPh sq 128
|length error: ic
| MAT=:(h,w)$_3 ic,|.@(4&{.)("1)_8]\3 ic,x
JVERSION
Engine: j806/j64/darwin
Release: commercial/2017-11-06T10:20:33
Library: 8.06.09
Platform: Darwin 64
Installer: J806 install
InstallPath: /users/brian/j64-806
Contact: www.jsoftware.com
Oh, and while I am thinking of it, can you or anyone clarify the following
sentence from wikipedia. I think there are missing words or something in
the sentence.
https://en.wikipedia.org/wiki/Domain_coloring#A_structured_color_function
"Therefore, in a strictly monotonic continuous function that stretches the
whole range compromises the resolution of smaller changes in magnitude."
Don't feel a need to answer my questions. I am just out of my depth again.
On Tue, May 8, 2018 at 6:31 PM, Jose Mario Quintana <
[email protected]> wrote:
> > I've been completely silent on the J forums for the past few years
>
> You were silent for too long Ewart ;) Welcome back!
>
>
> > I am partially confused by Ewart's definition of the "critical line"
>
> Brian, the "critical line" is used in the context of the Riemann
> hypothesis; see [0].
>
> One way to get some insight into the behavior of complex functions is via
> domain coloring; see [1] and the first couple of graphs on the page [2].
> One can produce this kind of graphs using J thanks to Andrew Nikitin; see
> [3]; for example, try,
>
> viewrgb 8 ccEnhPh (zetahat"0) 20 * sq 256
>
> (where zetahat is from Ewart's script and the rest from Andrew's script)
> and compare to the two graphs mentioned above; see [2].
>
> References
>
> [0] Zeros, the critical line, and the Riemann hypothesis
>
> https://en.wikipedia.org/wiki/Riemann_zeta_function#Zeros,_
> the_critical_line,_and_the_Riemann_hypothesis
>
> [1] Domain Coloring
> https://en.wikipedia.org/wiki/Domain_coloring
>
> [2] Riemann zeta function
> https://en.wikipedia.org/wiki/Riemann_zeta_function
>
> [3] Andrew_Nikitin/Phase_portraits
> http://code.jsoftware.com/wiki/User:Andrew_Nikitin/Phase_portraits
>
>
>
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