Mandelbrot to sound....

A while ago i posted some ideas on how to convert the Mandelbrot or Julia sets into sound. It didn't turn out so well, however, now i've finally discovered a way to make sound with these formulas, that might really be something. I'm not going to reveal the formula itself yet though, but i want you to try to guess what i've done. Just one hint, it involves no oscillators....

http://www.mediafire.com/?m0l080yrlnwu9t5

Hi Mats,

Am 04.10.2011 22:47, schrieb Mats �ljare:
> A while ago i posted some ideas on how to convert the Mandelbrot or Julia sets into sound. It didn't turn out so well, however, now i've finally discovered a way to make sound with these formulas, that might really be something. I'm not going to reveal the formula itself yet though, but i want you to try to guess what i've done. Just one hint, it involves no oscillators....
>
> http://www.mediafire.com/?m0l080yrlnwu9t5
>
>
Sadly, the link is not usable (broken?).
My browser could not connect to www.mediafire.com

:-( ...and I'm really keen to listen to it!

Best,
Wolf

The link doesn't work here, either.

--- In tuning@yahoogroups.com, Mats Öljare <oljare@...> wrote:
>
> A while ago i posted some ideas on how to convert the Mandelbrot or Julia sets into sound. It didn't turn out so well, however, now i've finally discovered a way to make sound with these formulas, that might really be something. I'm not going to reveal the formula itself yet though, but i want you to try to guess what i've done. Just one hint, it involves no oscillators....
>
> http://www.mediafire.com/?m0l080yrlnwu9t5
>

The link just worked for me. Very interesting sound. I'm going to
make a first guess at what Mats did with this -- does it have
something to do with wave terrain synthesis?

Jay

Quoting Juhani <jnylenius@...>:

> The link doesn't work here, either.
>
> --- In tuning@yahoogroups.com, Mats Öljare <oljare@...> wrote:
>>
>> A while ago i posted some ideas on how to convert the Mandelbrot or
>> Julia sets into sound. It didn't turn out so well, however, now
>> i've finally discovered a way to make sound with these formulas,
>> that might really be something. I'm not going to reveal the formula
>> itself yet though, but i want you to try to guess what i've done.
>> Just one hint, it involves no oscillators....
>>
>> http://www.mediafire.com/?m0l080yrlnwu9t5
>>
>
>
>

Well, i'm kinda disappointed noone came close to the solution, but here it is.

What i ended up doing is simply iterating the standard Mandelbrot/Julia squaring algorithm with a fixed number of iterations, around 20 in each of these examples, varying one of the parameters along a straight line and using the resulting value as the output level for each sample. You can either use the value of the last iteration, or add the value of all iterations together, the later gives a more complex sound which is what i used for most of the examples in the sound file.

This algorithm works with "inside" points only. This makes it rather limited, because not only is it limited to straight lines that contain inside pixels only, but most of them don't even give any audible result, for example the main bulb of the Mandelbrot set. There are only a few certain areas that have anything going on with them to give a audible result. Most of the samples i did are either of the "antenna" on the real axis of the Mandelbrot set, or the Julia sets from it. I would try with the power of 3 Mandelbrot, but i can't find a formula for it anywhere!

I also tried the "Mandelbar" and "Burning Ship" variants, but since these are the same for real numbers anyway, there's not much point to it.

There is one other formula i used however, which is the first one you hear in the sound example. That is simply a nested sine function, instead of squaring, with multiplication increasing with time. I included this because it was my first idea, and i think it's somewhat related to the Mandelbrot/Juilia formula.

I kind of imagined this having potential to be developed as a purpose made app, that lets you choose a path graphically along the M or J-set along with the other parameters, to render into audio. However upon trying this i have to conclude that there really isn't much more to find, than what is included in this sound file.

For those who really wonder, the ones that sound somewhat repetive are Julia sets from the real axis, the one that is just a single sliding pitch is -2 if i remember right, while the Mandelbrot ones sound more chaotic. Of course the difference between the "Julia" or "Mandelbrot" here is just what parameter is changed over the course of time!

But what really surprises me is how similar the results sound to sine waves, sometimes phase/frequency modulated sine waves. Is there a obvious relation between the squaring formula and the sine function that i've missed?

Mats Öljare <oljare@...> wrote:

> This algorithm works with "inside" points only. This
> makes it rather limited, because not only is it limited
> to straight lines that contain inside pixels only, but
> most of them don't even give any audible result, for
> example the main bulb of the Mandelbrot set. There are
> only a few certain areas that have anything going on with
> them to give a audible result. Most of the samples i did
> are either of the "antenna" on the real axis of the
> Mandelbrot set, or the Julia sets from it. I would try
> with the power of 3 Mandelbrot, but i can't find a
> formula for it anywhere!

The power of 3 Mandelbrot equation is z[n+1] = z[n]^3 + c.
Happy? Pari will even give that in terms of z[n] = x + iy:
x^3 - 3*x*y^2 + i(3*y*x^2 - y^3).

> I also tried the "Mandelbar" and "Burning Ship" variants,
> but since these are the same for real numbers anyway,
> there's not much point to it.

I don't know these, but second degree variants tend to be
warped versions of the true Mandelbrot set. I see
Wikipedia shows a Mandelbrot midget in the tricorn (which
it says is the same as Mandelbar). The third degree set
heads towards chaos faster, which might be important.

> But what really surprises me is how similar the results
> sound to sine waves, sometimes phase/frequency modulated
> sine waves. Is there a obvious relation between the
> squaring formula and the sine function that i've missed?

You know about period doubling cascades, right?

Graham