If you look back in the history of that page, that sentence showed up in this edit:
https://en.wikipedia.org/w/index.php?title=Domain_coloring&oldid=816967663 which had the edit comment "got all text from both merged articles" and which had that sentence as: "Therefore, it a strictly monotonic continuous function that stretches the whole range compromises the resolution of smaller changes in magnitude." And then a later editor tried to fix the grammar by changing "it" to "in". Which I guess does fit some grammar rules better, but doesn't show any comprehension of the material. So.. anyways... I imagine I might have edited the sentence to read something along these lines: "Therefore, it is a strictly monotonic continuous function which stretches the whole range [of something] and fits into the resolution [of the color diagram] using smaller changes in magnitude." I'd have to go back over that a few times to see if I could pick up an "it" which makes sense, and maybe also come up with something sensible for the bits I bracketed. I hope this helps... (and I hope I haven't further distorted the original meaning of whatever concept was being pulled in from wherever). Thanks, -- Raul On Thu, May 10, 2018 at 1:29 PM, Brian Schott <[email protected]> wrote: > 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 >> >> >> > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
