draw arg of the complex Zeta function

[primer]

Hello,

This morning I decided to graph arg of Zeta function.
Let me share with you how I easily build it thanks to hpprime with few line of program.

I wanted to see how Zeta function were extended to complex numbers in HpPrime.
Idea came from a picture from this video.

Ok, let's start.
To do this, I first had to create a function that would return a color from a number from [-pi ; -pi]
this function will take the argument, and will return a color.
for that I made a small program : a2c

Code:

EXPORT a2c(A)
BEGIN
LOCAL R,G,B;
 R:=127*(SIN(A)+1);
 G:=127*(COS(A)+1);
 B:=127*(SIN(A+π)+1);
 RETURN RGB(R,G,B);
END;

and here is how R,G and B will be computed with this function :


Next I needed to "see" it working with the full complex plan.

Code:

EXPORT testc()
BEGIN
LOCAL M:=40,P:=100;
FOR X FROM −M TO M DO
 FOR Y FROM −M TO M DO
  IF X≠0 OR Y≠0 THEN
   PIXON_P(X+P+M,Y+P+M,
   a2c(ARG(X+i*Y)));
  END;
 END;
END;
FREEZE;
END;

it gives that :


and I just need to made few change to get the Zeta :

Code:

EXPORT testz()
BEGIN
LOCAL M:=40,P:=100,Q:=10,K;
FOR X FROM −80 TO 15 DO
 FOR Y FROM −40 TO 40 DO
   K:=approx(CAS.Zeta((X+i*Y)/Q));
   IF K≠0 THEN
   PIXON_P(X+P+M,Y+P+M,
   a2c(ARG(K)));
  END;
 END;
END;
FREEZE();
WAIT();
END;

that gives :

note : on real calc, it takes about 7 minute to draw it, and at the end the calc will probably switch off (depending on your TOff).

note : CK "monitor" feature does not really respect colors displayed on real calc, I had to copy programs to virtual calc to have nice screen capture.

Regards,
primer.

[primer]

And while testing in virtual calc, as it's fast enough,
here is a wider view :


bye.

[primer]

And that's also fun to try other functions,

like :

is arg(x^(iY))

quite fast on real hpprime, btw.