I am glad to hear that it runs on JQt/Linux. It also seems to run on JHS
(at least it works with a Kindle Paperwhite 3 running on JHS/Linux
(BusyBox) using a custom J interpreter).
You might find the following clumsy verb useful,
domain=. |.@|:@({.@[ + ] *~ j./&i.&>/@+.@(1j1 + ] %~ -~/@[))&>/
It produces the vertices of a square grid corresponding to (the lower and
upper points of) a given complex interval and resolution; for example,
domain _1j_2 1j2 ; 0.5
_1j2 _0.5j2 0j2 0.5j2 1j2
_1j1.5 _0.5j1.5 0j1.5 0.5j1.5 1j1.5
_1j1 _0.5j1 0j1 0.5j1 1j1
_1j0.5 _0.5j0.5 0j0.5 0.5j0.5 1j0.5
_1 _0.5 0 0.5 1
_1j_0.5 _0.5j_0.5 0j_0.5 0.5j_0.5 1j_0.5
_1j_1 _0.5j_1 0j_1 0.5j_1 1j_1
_1j_1.5 _0.5j_1.5 0j_1.5 0.5j_1.5 1j_1.5
_1j_2 _0.5j_2 0j_2 0.5j_2 1j_2
In particular,
viewrgb 12 ccEnhPh zetahat"0 domain _20j_30 20j30 ; 0.1
reproduces, to some extent, the first graph on the Wikipedia page for the
Riemann zeta function. The leftmost section of the graph produced by J
looks suspicious and might indicate that Ewart's default approximation
(zetahat) breaks down at that point (or rather, at that line).
On Sun, May 13, 2018 at 2:04 PM, Brian Schott <[email protected]>
wrote:
> Pepe,
>
> Yes, I get no error with the script using jQt, so I can explore more.
> Your descriptions of the graphs helped me a great deal. Now maybe I can
> explore better.
> Thank you very much for your clear explanations.
>
>
> [snip]
>
> > I do not recall modifying Andrew's script in any way (apart from using
> just
> > a portion). Perhaps, other members can verify whether it works, or does
> > not, on Linux and Windows.
> >
> > Incidentally, the first graph "z, identity" (]) illustrates how the
> domain
> > coloring technique displays the complex plane (the straight lines are the
> > isophase lines (separating eight shades of the colors of the spectrum,
> from
> > red to violet, in the usual anticlockwise phase/angle order); the
> > circumferences are the isomagnitude lines. Together, the isomagnitude
> and
> > isophase lines, form a mesh similar to a spider web.
> >
> > This graph can be used as a key when trying to interpret the domain
> > coloring of other complex functions; for example, Andrew's second graph
> > "Exponent" (^) can be thought of as transforming the spider web coloring
> of
> > the complex plane into a quadrangular mesh: the horizontal lines must be
> > the isophase lines (because they separate (eight) shades of the
> spectrum);
> > consequently the vertical lines must be the iso magnitude lines (and they
> > are evenly spaced because,
> >
> > NB. Magnitude blocks are logarithmic and have light gradient toward
> > NB. increase.
> >
> > ). (It is interesting to note that the transformed isomagnitude and
> > isophase lines are still perpendicular at their intersections.)
> >
> > The ccEnhPhGray graphs also use shading intensity to convey information
> > about the image of a complex function; for example, the neibourhood
> around
> > the pole (in the center) of Andrew's second ccEnhPhGray graph looks
> > different from the zeros.
> >
> > I hope that you can be able to run eventually Andrew's script without any
> > errors and these hints can help you when your spouse is not around.
> >
> >
> >
> ----------------------------------------------------------------------
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>
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