A new visualization tool for OEIS sequences

[Dr George Whale]

Hello all, I've just joined SeqFan, and thought I'd introduce myself.

Let me confess first of all that I'm not a mathematician - my background's in art/design and software development.

A while back, I began developing an app to visualize character / number sequences as line drawings. I was using production (string rewrite) systems to generate sequences, but the results were mostly uninteresting due, I think, to limited variety in the output. Then I discovered OEIS!

The new version of the app (developed with my capable assistant, Claude.ai) transforms OEIS sequences into polyarc curve drawings. Some are chaotic-looking, others surprisingly structured - begging the question: do such visualizations tell us, at a glance, anything useful or significant about the structure and character of the underlying sequences?

The (free) app is called NCurve, and you can try it out here:
https://openprocessing.org/@GeorgeWhaleResearch/2986029
(Hint: press the 'New sequence' button repeatedly to search for interesting forms.)

Feedback (positive and negative!) welcome.

George Whale.

[Bill McEachen]

After fiddling with it a bit, my favorite so far is one added by Dr Sloane:

[George Whale]

That's a nice one. I might add a gallery of favourites alongside the app, if I can find a way to do it.

--
You received this message because you are subscribed to a topic in the Google Groups "SeqFan" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/seqfan/vGfMma6DkDk/unsubscribe.
To unsubscribe from this group and all its topics, send an email to seqfan+un...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/seqfan/47704c38-ac34-4a59-abb0-ed51369aa4ebn%40googlegroups.com.

[George Whale]

Hi Bill

I now have a small gallery, including your find: https://openprocessing.org/@GeorgeWhaleResearch/2986585

Best

George

[bill.m...@gmail.com]

Dr Whale:

Only becuase you wrote again, I attach other images I had found interesting (eye of the beholder) and saved off the other day.

Your gallery is great.

I cannot imagine the visualizations wouldn't provide useful insight in many cases.

I give "names" to most of them, and as you can see I iterated no parameters.

A376  French curve

A464  pie crust

A828  propeller

A1051  tire

A1553  saw blade

A1571 - ??

A1603 - ??

A39188  record disc

A39685  zipper

A39970  Slinky

Cheers

You received this message because you are subscribed to the Google Groups "SeqFan" group.
To unsubscribe from this group and stop receiving emails from it, send an email to seqfan+un...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAFDKQkGXaD2ncmf%3D5DL6CdtNw%3DbeGoxq3WZQCmwDNagUyN9ifg%40mail.gmail.com.

[George Whale]

Thanks, these will help expand the library. I like your idea of giving them concise names, but with nearly 400,000 sequences in the OEIS, and the average vocabulary only around 25,000 words, it could become challenging!

Best

George W.

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAKW3Wm4z6vWf8zkP5%2BXj_eeDp4YJ8xcOk4KZpw%3DO7TmPY613ug%40mail.gmail.com.

[jpallouche.math]

Hi

For similar ideas and pictures in more ancient papers (in the 1980's), 
please see

F. M. Dekking, M. Mendès France, Uniform distribution modulo one: a geometrical 
viewpoint, J. Reine Angew. Math. 329 (1981), 143–153.
[cf. pp. 149 and 151]

J.-M. Deshouillers, Geometric aspect of Weyl sums, in Elementary and 
Analytic Theory of Numbers (Warsaw, 1982), Banach Center Publ., 17, 
PWN, Warsaw, 1985, pp. 75–82.
[available at https://bibliotekanauki.pl/articles/721340.pdf
similar pictures in all pages but the first]

Actually I did not have the time to check whether these two references
are somewhere in the OEIS, may be they are not.

best wishes
jean-paul

You received this message because you are subscribed to the Google Groups "SeqFan" group.

To unsubscribe from this group and stop receiving emails from it, send an email to seqfan+un...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAFDKQkGXaD2ncmf%3D5DL6CdtNw%3DbeGoxq3WZQCmwDNagUyN9ifg%40mail.gmail.com.

[George Whale]

Bonjour Jean-Paul

Thank you so much for these references (from the 1980s!). I've been thinking of writing a short paper, and these will certainly help contextualise my efforts.

Best regards

George W.

To view this discussion visit https://groups.google.com/d/msgid/seqfan/c4caee75-cd41-47ef-bb6c-0251e21c4e1e%40gmail.com.

[Lisa Vitolo]

This is very cool, I've been looking at different sequences for an hour now :)

I'm thinking these would work nicely as wallpapers (for either laptops or smartphones), but I have to play with font size and aspect ratios a bit. And maybe add a black background and introduce more colours...

- Lisa

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAFDKQkFu%3DePB7a71vpfGzFEUeVC_AQNLJ80mP8Oj_LR5%3DsVb5g%40mail.gmail.com.

--

The Cockroach King of guile and greed
With a broken crown he's left to bleed
An empire falling to its knees
A bleeding ground for those who heed

[George Whale]

If you Export SVG then you can change line weight, colour etc. (using a vector app such as Illustrator or Inkscape, which is free), even combine several drawings together.

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAJy2vLF6Vh02kt11EdjgBy-943ue3KvU6x%3DV65QBeooswX1Ltw%40mail.gmail.com.