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

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  • 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 1 of 6 , Sep 4 11:28 AM
      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 2 of 6 , Sep 4 1:48 PM
        --- 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 3 of 6 , Sep 4 4:30 PM
          > 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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