## Re: An Improved Definition of Fractal Music?

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• 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]
• ... 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

Now, hopefully, back to making music!

Shawn
• ... 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
>
> 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
• ... 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

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

>Now, hopefully, back to making music!