Sound wave generation from 1D Mandelbrot formula

[Kali]

Well, you may want to take a look at this thread to know where this come from...

http://www.fractalforums.com/mandelbrot-and-julia-set/mandelbrot-on-real-numbers-t5375/

But this is the brief story: I was "researching" (Ok, that sounds too serious, I was just fooling around), the images generated by taking two 1D Mandelbrot functions (using real values), iterating with x, y values and then evaluating the combination of it's results.
At some point, tweaking some parameters, specially the way of evaluating the escape-time condition, I got this:



As it looked like a waveform, specially a sound waveform as any sound editing software shows it, I decided to look for some way of reproducing it.

First I had to figure out how it was generated, and after doing some math and research, I found that the shapes comes from the 1D mandelbrot formula "bifurcation map". To obtain this graph, the standard z=z*z+c is evaluated for each x real axis value and the results after each operation, are plotted in the Y-axis.

So this is it:



In this video and with a VB.NET application I wrote to obtain the waves, I explain how they are generated.

(watch fullscreen)

<a href="http://vimeo.com/moogaloop.swf?clip_id=19199378&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA" target="_blank">http://vimeo.com/moogaloop.swf?clip_id=19199378&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA</a>

(When I say the "Fractal wave", I mean "the soundwave-like graph that I got by accident from drawing a fractal". I'm not affirming that the waveform it's a fractal itself, just a way to call it for the people who was following my posts. Also there is a mistake, the wave is not generated by taking the max and min values, but the closest positive and negative values to the x axis)

Then I managed to make a .raw file from my program, that Sound Forge can read.

This are the first results:

http://www.megaupload.com/?d=7H56GOP7

http://www.megaupload.com/?d=L19JKJ42 (this one has better quality)

So... what you think? it definitely sounds weird 

As they are some parameters that can be tweaked (the segment of the line used, the iteration rate, etc.), I will be posting other results soon.

[Fractal Ken]

Really neat work! The 2nd .mp3 makes me think of gusty winds.

[Kali]

Thanks Ken, and you are right... it sounds something like that.

Now that I already listened to that waveform I got by accident, I decided to try another ways of combining the data from the bifurcation map.

This is what I get with an additive synthesis of the waves I get after some iterations:

The bifurcation map with the result in yellow


The wave extracted


The sound:
http://www.megaupload.com/?d=VWJLDTW3

It's pretty similar, but now as it is made from sinewaves, the sound is smoother and more clean.

I'll be trying other synthesis methods...

[Sockratease]

Nice work!

I may have a go at converting these "raw" sound files to Music using my Secret Weapon program I use to make all the music in my Fractal Videos   

I never made the part 2 of my original effort using the silly jpg to wav converter, but the process is identical.  In fact, most of the music I make starts off as a wav file of Lissa talking 

If anyone cares, I'll make that second video - otherwise I'll just keep the process to myself  (the music isn't really very good, but it's a fun process and I wanted a way to make music that wouldn't violate any copyrights).
I am enjoying this effort though - it's quite an entertaining distraction 

[Kali]

I was seeing some of your videos and music isn't bad, there are pretty interesting sounds that fits ok with the images.

Feel free to use the sound files as you want, and keep creating!

(it must be easy to create things with such a beatiful muse next to you   )

[KRAFTWERK]

Wow, you did it Kali!

I just heard the very first sample, and recognised it from KRAFTWERK:s "Geiger counter" from the album "Radioactivity"
Listen 0:48 in to it: <a href="http://www.youtube.com/v/VPymqvtbFSA&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/VPymqvtbFSA&rel=1&fs=1&hd=1</a>

Scaaary...

[Kali]

Awesome coincidence!

[jehovajah]

Really neat work! The 2nd .mp3 makes me think of gusty winds.

Well spotted Ken! I have to agree. Wind gusts are based on vortices passing through the observers hearing boundary. The crazy thing is these variations in sound are driven by temperature and pressure variations which though not totally random are stochastic, in the sense they simulate the whirling of gas pressures through the hearing  boundary. So does this sound represent the whirling of the complex factors past the x axis?