Mandelbrot on real numbers (new post)

[Kali]

@Sockratease: Nice try, and the program is cool but it doesn't convert the waveform to audio, it just uses any JPG to produce sound out of it.
I tried to get a proper soundwave image, but it allways looks like a compact waveform just like any audio editing software shows when it maps a wave file to show it entirely on screen, but if I zoom or stretch the fractal to get better resolution, it just doesn't look like waves at all.

Anyway, here's a better resolution image: (it's bigger than the size the forum shows)



It's still kind of fun to make sounds with that program, thanks for let me know of it  

@Ken I'm also a little bit musician but I think that even the fractal do better than me  

[Sockratease]

Thanks, Ken & Kali.  Glad you found it amusing  

I tried to make clear that the software just uses jpg data and not the waveform's image.  I doubt any procedure exists to get "true" sound from just an image of a waveform.  Still, it's based on the waveform!

I'll turn it into something more musical tonight and post the results later.

Meanwhile...

I found this as a "suggested" video on youtube on the same page my video was on:

<a href="http://www.youtube.com/v/3Br57CsDAFw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/3Br57CsDAFw&rel=1&fs=1&hd=1</a>

It's the Mandelbrot Set converted to sound using a much better system.

From the author:

Sonification of the Mandelbrot set fractal. Composed by Gustavo Díaz-Jerez.

Procedure:

- X axis of image mapped to time, in seconds.

- Y axis of image mapped to frequency (27.5 - 4163Hz, continuous, exponential scale, using sinusoids).

- Brightness of image mapped to dynamic range. Black (0,0,0) = silence (-INF dB). White (255,255,255) = Max (0 dB)

The right side shows a spectrogram and a bar diagram of the sound. The bottom shows the wave form.

Postprocessing: bass frequencies boost.

Notice that this is not somehow inspired or "based" on the image. It IS how the image translates to sound for the given paramenters.

I think this subject bears further investigation...

[trafassel]

Here the remaining pictures of the original formula in this thread (Bailout: abs(x-y+z)  ).

Same scene in small and high iteration.

[trafassel]

...

[bib]

We've got something really new here, and super funky colors 
Bravo Herr Doktor Trafassel!

[Kali]

Very beatiful and interesting pictures, trafassel!


Today I tried to understand the "bifurcation maps" I posted, and I tried this with just one 1D formula;
Here's the plot of the values after each iteration placed on the Y-axis, for each real value on the X-axis.



So this is where the bifurcation maps I got come from.

But it seems like it's something already known, as I was reading in some old forum's posts.

Now I will look for the "soundwave" again, if I have some time. I think it's still a wave but made of strange polygons, that stretches very fast in the X axis. I have to deal with bailout and iteration values, and the formula itself to make a decent waveform image, an then I know how to get the values for making it sound!

Wish me luck...

[paolo]

  Here is a new picture to feast your eyes on. There is a parameter file to generate it at a higher resolution if you have Ultra Fractal. Sorry it is not in colour and it is not my formula.

[Kali]

I wrote a program in VB.NET and I made a video that speaks for itself  

(click on full screen to watch it properly)
<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>

Tomorrow I'll try to get a .wav file

[Fractal Ken]

Great job, Kali! I like the iteration-by-iteration view. The video in your post is kind of small, but it looks real good on Vimeo.

[Kali]

Thanks Ken! I made this to show how the first images of the wave were generated (by accident). I had to think a lot to figure out this, because the first images where generated in ultra fractal and what happened is that the way I evaluated the bailout condition made a image similar to what you get if you plot the iteration values placed on the Y-axis (the 2D bifurcation maps), but I didn't understand at first why the waveform patterns emerged.

I'm looking for a way to generate a sound file with the values, I'll read some documentation on generating .WAV files and try it later.
Don't know if it will work, I must see how to take the values because they aren't just like a standard waveform when you zoom in, but I think I'll figure out a way to reproduce some sound out of it.

Anyway, I'm interested on working on the real waves that forms the bifurcation pattern (you can see them in the video as the iteration count ascend), there must be a proper way of combining them to make something more close to a "fractal waveform".

I'll work on this if I have some time today and maybe I'll open another topic for posting the results.

Bye!

[Kali]

Ok, last post about the waveform inside this topic... I'll start a new topic as soon as I get the sounds.

But here's the processed data to make a proper soundwave

First I detected all the wave "depressions" (don't know if I should call them that way, but seeing the image you get the point)



Then I copy each segment of the wave, and added a copy after that segment but with inverted values.



So I have sampled the wave, now I have to make it sound... I'm looking for a .wav library for vb.net to make it easy, otherwise I have to learn the structure of a .wav file to generate it with my own code.

Meanwhile, if you want a text file with some raw data, just ask me.

[KRAFTWERK]

This is so crazy Kali.
I love it! 

PSSSSCCCCHHHHHHHHHHHHHHH

Probably, but what if...

[Kali]

Yeah, I know it's pretty crazy 

I don't really take this too seriously and I neither have too much expectations as for the results but at least it's a fun way to practice VB.NET programming (I'm an old school VB6 programmer and I'm just learning .NET).

And it's out of curiosity too...

But... as you said: what if?... 

[Kali]

For those who are interested, I finally get the sound files of the waveform.

Further posts for this research will continue here:

http://www.fractalforums.com/new-theories-and-research/sound-wave-generation-from-1d-mandelbrot-formula/

Thank you all for showing your interest

Bye!

[jehovajah]

I'm going to take a shot at expanding on Mike's suggestion: presenting general formulas which encompass both the Mandelbrot set and Kali's ideas.

     Iterate (x, y) = (f(x, y), g(x, y)) + c
     Stop if h(x, y) > b

x and y are real variables [(x, y) is complex; typical notation would be z = (x, y)]
f, g, and h are real-valued functions
c is a complex constant [pixel dependent in the Mandelbrot case; pixel independent for Julia's]
b is a real constant [the bailout threshold]
 
For Kalibrots : f(x, y) = x², g(x, y) = y², and h(x, y) = |x - y|.

For the Mandelbrot set: f(x, y) = x² - y², g(x, y) = 2xy, and h(x, y) = sqrt(x² + y²) [the modulus].
Note: You get f and g by using the definition of complex multiplication to compute z², where z = (x, y).

Please excuse my mistakes and imprecisions; I'm a rusty mathematician trying to balance simplicity against generality.

Ken

Just to say Ken has it on the money. Deeper(unecessary) explanation and ( suggestive) exploration start here