[seqfan] Re: Wanted: suggestions of new sequences for poster

Georgi Guninski guninski at guninski.com
Sun Nov 25 10:44:03 CET 2012


Got some knew ones, including colored circles.

Define x,y=inverse_cantor_pairing(n) - this appears related to:

A048147 Array T read by diagonals; T(i,j) = i^2 + j^2.

a(n)=x^2+y^2 mod 2^11 gives circles both in grayscale and
colormap prism_r.
a(n)=x^4+y^4 mod n gives something remotely resembling fractals.

Uploaded the new images.
The color circles are:
x^2+y^2 mod 2^11 colormap prism_r maybe A048147 mod 2^11.png

Most of them look better when looked at smaller ratio.


On Sun, Nov 25, 2012 at 10:31:50AM +0200, Georgi Guninski wrote:
> Here is an idea for plotting sequences in 2d.
> 
> Chose a bijection f: N^2 -> N (I experimented with Cantor pairing).
> Set the "value" of (x,y) to a( f(x,y) ).
> Interpret the "value" as color. If working with grayscale,
> smaller is darker. You can map to RGB or HSV.
> Probably sequences with small range are better.
> 
> I experimented with a(n):  n mod 2, n mod 5, is_prime(n), sigma_0(n)
> and in sigma_0(n) got diagonal structure that if true is strange to me.
> 
> Here are some examples in sage (can't set legend yet so read the
> name).
> http://stefan.guninski.com/oeisposter/
> 
> 
> Note that the png images might contain compression artifacts
> and I might well have screwed the coding/logic...
> 
> For other ideas check this mathoverflow post (discussing compression
> visual artifacts):
> http://mathoverflow.net/questions/77794/ascii-prime-plots-and-prime-rich-quadratic-polynomials
> 
> On Sat, Nov 24, 2012 at 06:57:44PM -0500, Neil Sloane wrote:
> > Dear Seq Fans, 3 years ago David Applegate and I made
> > a poster to celebrate the birth of the OEIS Foundation.
> > It contains 25 of my favorite sequences (you can download it
> > from the OEIS Foundation web site, http://oeisf.org).
> > 
> > I would like to make a new poster, to give out at the big
> > AMS meeting in San Diego in January. Can people send me
> > suggestions of sequences that have been added to
> > the OEIS in the past couple of years that would
> > be good material for the poster? Naturally sequences that
> > have a striking image associated with them are especially welcome.
> > 
> > Neil
> > 
> > _______________________________________________
> > 
> > Seqfan Mailing list - http://list.seqfan.eu/
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/


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