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Re: [PrimeNumbers] Hashing the positive integers into graphic art.

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  • Phil Carmody
    ... It s pretty cool. The idea of creating bijections between numbers and multi-dimensional images is one I ve theorised about a lot (I was going to turn DeCSS
    Message 1 of 6 , Sep 3, 2006
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      --- Roahn Wynar <rwynar@...> wrote:
      > You can have a look at the idea on a small site I built just for this
      > purpose: https://home.comcast.net/~rwynar/. I will add an applet to generate
      > these images soon, I just have to convert my little java code into applet
      > form.
      >
      > Of course all comments are welcome.

      It's pretty cool. The idea of creating bijections between numbers and
      multi-dimensional images is one I've theorised about a lot (I was going
      to turn DeCSS into a real (acrylic on canvas) Mondrian-style painting,
      for example). I don't suppose you could add an alt-tag to each image on
      the web-page, indicating what number it represents could you?

      Phil

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    • Chris Caldwell
      ... Very nice. I wrote a script to draw some of these and see why you chose to work with the largest factor first (though I used a green square instead of a
      Message 2 of 6 , Sep 3, 2006
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        > --- Roahn Wynar <rwynar@...> wrote:
        > You can have a look at the idea on a small site I built
        > just for this purpose: https://home.comcast.net/~rwynar/.
        > I will add an applet to generate these images soon, ...
        > > Of course all comments are welcome.

        Very nice. I wrote a script to draw some of these
        and see why you chose to work with the largest factor
        first (though I used a green square instead of a circle
        in a square for the third terminating image). I made
        some animations, but none very interesting...

        There are obviously easier ways of converting
        numbers to images, but that one is fun and is much
        nice looking!

        Chris





        A couple quick notes on the longer article (you should
        probably ignore these, I'm not as artistic as you...):

        You left out 2, and 3 in abstract. Def 2.3 does not need infinity
        if it is as stated the index of prime (only), maybe reword the
        sentence before the def to apply to all n. Typo n for
        p in same def. In (5.2) write 37 not 39. ... In def
        (2.4) make don't call 5 a large prime; add ref to 2 as flat,
        3 as sharp rather than just imply it defs 2.1, 2.2.
        In the intro 10472 is not prime. You refer to the
        wrong figure there. Much of the verbiage of the first
        few paragraphs should be removed as distracting from
        what you achieved (especially the notion of "equal size,"
        self deprecation like first sentence of third paragraph...)
        Simplify. It is too nice of idea to bury in words.

        Overall your artistic nature may have gotten too strong
        of hold on you. If I was a referee I'd suggest you simplify
        the notation to what you have in figure 2; that is use [n]
        as in the image instead of #FKA(n). The sharp, flat and
        natural operators may be more readable as function notation
        (and perhaps subscripts to indication iteration), but
        could be left to save effort.
      • Roahn Wynar
        For those who are interested, you can now experiment with the Whole Number Hash Applet at https://home.comcast.net/~rwynar/. You can input some pretty big
        Message 3 of 6 , Sep 4, 2006
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          For those who are interested, you can now experiment with the Whole Number Hash Applet at https://home.comcast.net/~rwynar/. You can input some pretty big numbers since the Applet uses BigInteger arithmetic, but be careful, for now the factorization method is pretty lame and if you put in primes over about 7 digits things can take a while. That is pretty embarrassing, considering this list's distinctiveness regarding factoring. I promise to fix this in V1.1 :).

          Phil - I have added a Java Applet at https://home.comcast.net/~rwynar/ , which is probably even better than control-click. If you have a truly exotic number you would like converted I would happily give it a go.
          Chris - I would enjoy seeing how your script outputs looked. Is there anyway to send a sample on to me? In my algorithm the borders of the atoms get demagnified with the atoms which gives a slightly uneven appearance (that is...the borders at each recursive level are not all consistent.) However this effect is useful for tracking the recursion depth by eye, so I have not bothered to work that issue out. I am wondering if your script naturally handles this.
          What sort of animation did you attempt, that sounds interesting. Thanks for your comments on the paper, they are all excellent. I was certainly aware of the verbosity problem, which is why I wrote the short version, which is STILL verbose. I am no fan of pretentious notation, so I will be taking much of your advice.

          Roahn

          [Non-text portions of this message have been removed]
        • Phil Carmody
          ... Oh dear, you seem to have fallen for the write once, run anywhere bu^Wmarketting message that Sun was so proud of. Alas, it don t work here, and yes,
          Message 4 of 6 , Sep 4, 2006
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            --- Roahn Wynar <rwynar@...> wrote:
            > For those who are interested, you can now experiment with the Whole Number
            > Hash Applet at https://home.comcast.net/~rwynar/.

            Oh dear, you seem to have fallen for the "write once, run anywhere"
            bu^Wmarketting message that Sun was so proud of. Alas, it don't work here, and
            yes, before you ask, my VM came from Sun. (It's alive, it *_VERY_ANNOYINGLY_*
            pulls the window to the top of the window-manager's z-stack when my mouse even
            glides past the applet, it just doesn't do anything.)

            > You can input some pretty
            > big numbers since the Applet uses BigInteger arithmetic, but be careful, for
            > now the factorization method is pretty lame and if you put in primes over
            > about 7 digits things can take a while. That is pretty embarrassing,
            > considering this list's distinctiveness regarding factoring. I promise to
            > fix this in V1.1 :).

            P-1 and Rho are really simple. I recommend just throwing in a quick
            implementation of one or the other. If there's a built-in modular expmod for
            bignums, then probably P-1 will be most efficient. Otherwise, you really can't
            get simpler than a Rho, implementation-wise. (And do the Brent version, as it
            has handy stopping points for factor checking.)

            Phil

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          • Chris Caldwell
            ... I d wondered if you did that on purpose. Go to http://www.utm.edu/staff/caldwell/preprints/temp/ 1to30 is just that, 1, 2, 3, ... Then the flat primes p,
            Message 5 of 6 , Sep 4, 2006
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              > Chris - I would enjoy seeing how your script outputs looked.
              > Is there anyway to send a sample on to me? In my algorithm
              > the borders of the atoms get demagnified with the atoms which
              > gives a slightly uneven appearance (that is...the borders at
              > each recursive level are not all consistent.) However this
              > effect is useful for tracking the recursion depth by eye, so
              > I have not bothered to work that issue out. I am wondering
              > if your script naturally handles this.

              I'd wondered if you did that on purpose. Go to

              http://www.utm.edu/staff/caldwell/preprints/temp/

              1to30 is just that, 1, 2, 3, ...

              Then the flat primes p, pq, pqr, ... to 307

              Then the same for the sharp.

              Made by quick and sloppy Maple, exported, made smaller
              with fireworks...

              Hope I did these right, didn't check very carefully...
              CC
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