- 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] - --- In cnfractal_music@egroups.com, "David Woolls" <davidwoolls@c...>

wrote:

> Reading Phil Thompson's site ... He also explains how he gets a

Yes. I hate to be persnickety (who, me?) but Phil's example has

>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?

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

My point was that, given the Mandelbrot's original, strict definition

> notes from the non-terminating set?

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?

I need to clear up some confusion here... Note that in my post, I

> 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.

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

Excellent observation! Remember: the source is math, not an image or

>beautiful noises or what you programmers do with them.

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

Yes, the M-set is the black spots, not the color spots. I don't care

>as a multicolour version but, if I have understood you, this has no

>effect on the representation of the Mandelbrot set itself.

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

Regarding the M-set pictures - When doing the Z<=Z^2+C iteratively

>untrue representation.

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

By now I hope it's clear that rules don't really apply. We are

>using the set, or indeed any other fractal if the same rules apply.

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

Asking questions is a good thing. We ALL learn from the interaction -

> ejected from the list???

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 - --- In cnfractal_music@egroups.com, Forrest Fang <ffcal@v...> wrote:

> >Shawn said:

interaction -

>

> >Asking questions is a good thing. We ALL learn from the

> > myself the most. You know how much additional stuff I've had to

right past

> >read to answer these questions the last couple of days?!?!?!

>

> Thanks for the clarification, Shawn, even if the pure math went

> me....

OK. I'll stop now. I really appreciate the time Shawn has taken as

>

> >Now, hopefully, back to making music!

>

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

>

> Forrest

>

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 >Shawn said:

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

>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?!?!?!

me....

>Now, hopefully, back to making music!

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

Forrest

<ps...glad you liked my new stuff!>>

> Shawn