Loading ...
Sorry, an error occurred while loading the content.
 

Re: An Improved Definition of Fractal Music?

Expand Messages
  • David Woolls
    Hi Shawn (and others still with us) ... Not so fast Mr Bulen :-)) I d like to understand this a little better before you run away. You said EVEN MUSIC BASED
    Message 1 of 13 , Aug 1 10:21 AM
      Hi Shawn (and others still with us)

      >>Now to get back to making music!

      Not so fast Mr Bulen :-)) I'd like to understand this a little better before you run away.

      You said

      EVEN MUSIC BASED ON THE MANDELBROT SET IS NOT FRACTAL.

      ... But the Mandelbrot set is the collection of mutated cardoid shapes and circles in the middle, not the pretty colors around it. So setting those pretty colorful regions to music is not fractal - it's not even a sonic representation of a fractal shape. In addition, music generated in this fashion is finite - non-fractal, and measurable via ordinary means.

      Reading Phil Thompson's site (who has stayed out of this so far) he explains how he gets the notes and colours from terminating calculations and explains that the non-terminating ones are part of the Mandelbrot set. He also explains how he gets a number between 0 and 12 for the notes. Presumably he can either get two notes from the two components between -2 and 2, or he can use one of the numbers to generate velocity, octave, duration or whatever by using a different factor on the number?

      Are you saying that the only fractal music is actually that using notes from the non-terminating set?
      If so, how much would get thrown away, generally speaking?
      Is it the non-fractal bits which make it sound beautiful so often or the fractal bits?
      If it doesn't terminate how do you know when to stop making music?
      I presume it is possible to determine mathematically that it is not going to terminate, but you must also have to decide that enough is enough in terms of notes generated.

      What I am wondering is whether it is the fractals that generate the beautiful noises or what you programmers do with them. A two-colour representation of the Mandelbrot set is not as pretty as a multicolour version but, if I have understood you, this has no effect on the representation of the Mandelbrot set itself. Any premature termination to give a colour would presumably be an untrue representation. Is the same true of the music generated using the set, or indeed any other fractal if the same rules apply.

      Or am I still on the wrong planet? Or worse, am I about to be ejected from the list???


      David










      [Non-text portions of this message have been removed]
    • Shawn Bulen
      ... Yes. I hate to be persnickety (who, me?) but Phil s example has pretty high rounding errors that confused me at first. The first few rounds through the
      Message 2 of 13 , Aug 1 10:24 PM
        --- In cnfractal_music@egroups.com, "David Woolls" <davidwoolls@c...>
        wrote:

        > Reading Phil Thompson's site ... He also explains how he gets a
        >number between 0 and 12 for the notes. Presumably he can either
        >get two notes from the two components between -2 and 2, or he can
        >use one of the numbers to generate velocity, octave, duration or
        >whatever by using a different factor on the number?

        Yes. I hate to be persnickety (who, me?) but Phil's example has
        pretty high rounding errors that confused me at first. The first few
        rounds through the Z<=Z^2+C should have been .5+.5i, .5+1i, and -
        .25+1.5i.

        > Are you saying that the only fractal music is actually that using
        > notes from the non-terminating set?

        My point was that, given the Mandelbrot's original, strict definition
        of fractal, if creating music from the Mandelbrot set, yes. This is
        usually called the 'bounded' set. But remember, he softened his
        definition and I softened mine... I did this late in my online
        soliloquy, and probably had either scared folks off by then or
        put 'em to sleep.

        > If so, how much would get thrown away, generally speaking?
        > Is it the non-fractal bits which make it sound beautiful so often
        >or the fractal bits?
        > If it doesn't terminate how do you know when to stop making music?
        > I presume it is possible to determine mathematically that it is not
        >going to terminate, but you must also have to decide that enough is
        >enough in terms of notes generated.

        I need to clear up some confusion here... Note that in my post, I
        described a different musical generation process than Phil T's.
        example. When I've seen the Mandelbrot set converted to music, the
        user draws a line through the colors, and the colors that the line
        crosses are played out as music. In my earlier post, I pointed out
        that the colorful regions are NOT the fractal portion - the black
        spots are. In Phil's example, you pick an individual point and
        listen to a melody as the iterations through the process are
        converted to tones. In Phil's example, if the point you pick is in
        the M-set, it can go on indefinitely.

        The basic underlying process is the same, however, that of applying
        the Z <=Z^2+C function in an iterative fashion. We've seen very
        different ways of translating that process into music. Which goes
        back to my revised definition of fractal music: focus on the process,
        not the Hausdorff dimension. Because the same underlying
        mathematical process is used in all these methods, whether converting
        the colorful regions to music or the black splotches to music...

        > What I am wondering is whether it is the fractals that generate the
        >beautiful noises or what you programmers do with them.

        Excellent observation! Remember: the source is math, not an image or
        a melody. A fractal computer artist has many options regarding how
        to translate the math to pictures, as evidenced by the many thousands
        of completely different representations of the Mandelbrot set out
        there. In a similar fashion, different fractal music programmers can
        use this infinitely comnplex source of information to derive
        different types of music from it. 10 of us can use the same
        underlying process, and produce 10 completely different results -
        even if provided the same 'point in' or 'line thru' the M-set.

        For example, I understand Yo Kubota's Mandelbrot Music will actually
        let you map the colors to microtones, not limiting you to a 12-tone
        scale!

        >A two-colour representation of the Mandelbrot set is not as pretty
        >as a multicolour version but, if I have understood you, this has no
        >effect on the representation of the Mandelbrot set itself.

        Yes, the M-set is the black spots, not the color spots. I don't care
        how many colors you use depicting the color spots, the black splotchy
        M-set maintains its shape.

        But down another rabbit hole: Who says the two-color pic isn't
        pretty? Peitgen's book ("Oh no, he's at it again!" - Rex, "Toy
        Story") has some incredible 2-tone shots of the M-set and the
        equipotential lines eminating from it. Translated to music, 2 tones
        may be beautiful on either a melodic instrument or a percussive
        instrument - think of all the wild latin 2-note coolness!

        >Any premature termination to give a colour would presumably be an
        >untrue representation.

        Regarding the M-set pictures - When doing the Z<=Z^2+C iteratively
        using complex numbers, some points start a series of numbers that
        drift off into inifinity (the unbounded, or escapee set - the
        colorful regions) and some points start a series of numbers that
        always hover between 2 and -2 (the bounded, or prisoner set - the
        black splotches, the M-set). The colorful regions are the unbounded
        set. At some point, you gotta stop it & give it a color. The colors
        are a measure of how quickly the point zips off to infinity.

        >Is the same true of the music generated
        >using the set, or indeed any other fractal if the same rules apply.

        By now I hope it's clear that rules don't really apply. We are
        making up the rules as we go along. We've found an apparently
        unlimited source of information, and different programmers choose to
        translate that chaotic stream of information to music using various
        means.

        > Or am I still on the wrong planet? Or worse, am I about to be
        > ejected from the list???

        Asking questions is a good thing. We ALL learn from the interaction -
        myself the most. You know how much additional stuff I've had to
        read to answer these questions the last couple of days?!?!?!


        Now, hopefully, back to making music!

        Shawn
      • David Woolls
        ... interaction - ... right past ... OK. I ll stop now. I really appreciate the time Shawn has taken as well as the work of the other programmers. Like
        Message 3 of 13 , Aug 1 11:04 PM
          --- In cnfractal_music@egroups.com, Forrest Fang <ffcal@v...> wrote:



          > >Shawn said:
          >
          > >Asking questions is a good thing. We ALL learn from the
          interaction -
          > > myself the most. You know how much additional stuff I've had to
          > >read to answer these questions the last couple of days?!?!?!
          >
          > Thanks for the clarification, Shawn, even if the pure math went
          right past
          > me....
          >
          > >Now, hopefully, back to making music!
          >
          > Good idea. Me head hurts!;)...
          >
          > Forrest
          >

          OK. I'll stop now. I really appreciate the time Shawn has taken as
          well as the work of the other programmers. Like Phil, I like what
          comes out but I do like to know what is going on, in so far as I
          can.

          David
        • Forrest Fang
          ... Thanks for the clarification, Shawn, even if the pure math went right past me.... ... Good idea. Me head hurts!;)... Forrest
          Message 4 of 13 , Aug 1 11:05 PM
            >Shawn said:

            >Asking questions is a good thing. We ALL learn from the interaction -
            > myself the most. You know how much additional stuff I've had to
            >read to answer these questions the last couple of days?!?!?!

            Thanks for the clarification, Shawn, even if the pure math went right past
            me....

            >Now, hopefully, back to making music!

            Good idea. Me head hurts!;)...

            Forrest

            <ps...glad you liked my new stuff!>
            >
            > Shawn
          Your message has been successfully submitted and would be delivered to recipients shortly.