Fractal Waveform?

[samuraipizzacat29]

I CAN HAZ MIDI FILES!!!!

nice work on that link. I guess none of us are intelligent enough to google it....

This thread really makes me want to mess with sampling noise now and messing with the sample points. there should be some good waves to be found that way.

[MitchXI]

If you've tried the early versions of Bazille from u-he, there is 'fractal resonance.' This is actually sync casio-style with an audio AM to smooth out the inharmonics.


If you want a 'fractal inspired' waveform that is still musically useful, you could preserve at least the zero crossings at the start and end of the waveform and then play around with the geometry of it.

- A cyclic waveform that increases in pitch but remains centered. So like normal hard sync except the waveform would stay centered and the endpoints of your wave would rise and fall with increasing 'fractal zoom'

- A triangle/sine/two-peak wave with sync points at the peaks and troughs. So increasing sync would generate inversions in the peaks and troughs.

- Any wave through an amplitude foldback function with bias. at bias of 0, 1, 2, etc. any integer bias you would have the original wave. In between, folded variations. You could even have a repeating pattern of gain to increase the complexity ( at values of #.5 max gain, integer values no gain)

feel free to call BS on any of this, I've done variations of these in puredata back when I was doing clumsy DSP


These aren't really very fractal, but complex sync patterns follow the heart of the idea to a degree, I think.

[DLovas]

Otherwise it's a bunch of balderdash.

"Balderdash"??

In an instant, I'm transported to Victorian England, populated by street urchins and upright gentlemen sporting fine moustaches -- VSE was in its infancy back then.

It would happen to be that, these topics, I find most entertaining in nature, not to mention I hold in the highest regard. The world of modern synthesizers lacks something with the elegance and simplicity of the object y
That you do describe. I shall search for this relic at once - an if that fails, which I have no doubt it shall, then at ye proper moment all shall mend itself. Off for some tea now

But seriously though - reminds me of the Hartmann Neuron in the way that it loads examples of sounds mapped mathematically - which are then able I be altered on the board for further sound creation. This was a very interesting topic idea - glad I saw it.

[impaler42]

MitchXI, that sounds pretty interesting. Id like to look into that method.

[Automatic Gainsay]

Ugh, okay. Do you realize that soundwaves are literally graphic representations of how things vibrate? As such, there are limitations on how those vibrations can be portrayed. A thing can only vibrate in a way that is possible for a thing to vibrate, and those vibrations... to generate soundwaves... must vibrate in shapes and frequencies that cause air molecules and/or electrons to vibrate similarly, and in frequencies and amplitudes that are audible to the human ear. Fractal patterns are not consistent with how objects, etc. vibrate. This whole conversation is speculative.

[silikon]

Not sure if this is the place, or if anyone cares, but this is a weird idea I had.
For those who don't know, a fractal is essentially a geometric figure that contains recursive, scaled versions of the same figure to infinity. In a waveform, this could be a triangle wave that's wavelength decreases as it approaches the center of the wave, and then increases wavelength as it reaches the end of the waveform. A synthesizer could theoretically produce this sort of wave by means of reducing it to a fractal algorithm.
I suppose something like this could be used for a tuneless noise oscillator, but it would be a lot cheaper to just use a single noise waveform and make it play on any key. This oscillator would also just be ping-pong frequency modulating, and it would probably sound like pressing the highest and lowest keys on a regular synthesizer with fast portamento. In conclusion, there's no real application for anything like this. Dunno

I didn't see any question mark at the end of your statement, so I feel slightly uneasy about responding. Plus, the idea of a fractal waveform in the strictest sense would be impossible to audibly describe due to the representation of every frequency at every amplitude, or even many frequencies at varying amplitudes. White noise?

One could probably say that additive synthesis does a good job of recreating a fractal waveform in 2 dimensions, and can be broken down from the larger "complete" waveform into individual yet identical elements.

...but then you would have to digress into the idea that every form of sound generation would be considered fractal...

Also, this could be considered fractal entertainment:

[Sir Nose]

A single cycle fractal waveform is just another single cycle waveform produced by the sum of the pieces (repetitions of the original). The scale of each repeated wave is important since many will result in an infinate amplitude somewhere in the final summed waveform. The decay rate needed to avoid an infinite spike in amplitude would force the wavelength to decay at the same rate and only change a small portion of the original.

[cornutt]

Ugh, okay. Do you realize that soundwaves are literally graphic representations of how things vibrate? As such, there are limitations on how those vibrations can be portrayed. A thing can only vibrate in a way that is possible for a thing to vibrate, ...

That was my first thought when I started to read this thread: are we talking about waveforms that look like a fractal on the scope, or are we talking about a sonic analog to a fractal? As AG points out, the former would be difficult to do in a manner that would come up with anything interesting, given that all the visual fractals I've ever seen rely on being in a 2- or 3-dimensional space, but an electrical signal that represents sound really only exists in one dimension (the other dimension being time, which we can't change). Now, you could might do something interesting with a scope in X-Y mode (consider: a spiral is a simple fractal), but that's different from actually hearing it. There might be some possibilities in considering stereo sound; our brains attempt to correlate the signals from our two ears in certain ways and it might be possible to play some games with that. I don't know enough about psychoaccoustics to say.

Considering the latter, that of something sonically analagous to a fractal, we already have one example of that: the Shepherd tone. Which actually has me thinking: suppose that, instead of just sweeping a Shepherd tone up or down like we usually do, we actually play a melody with it? Especially one that has octave-or-greater intervals? Hmm. I've got some a Shepherd generator I wrote in Csound. May have to play with that. Thinking along those lines, a conventional harmonic series is a "fractal in one direction" if you maintain a mathematical relationship between the harmonics. Hmm. Someone up-thread mentioned noise. I have a chaos theory textbook around here somewhere that talks about degrees of noise. We already know of white noise, pink noise, random walks, etc. There's more. I need to go dig that up.

[ItsMeOnly]

Actually, the visual representation: it would be a sawtooth wave
Another example I could think of would be a "fuzzy sine" - if you think of that, if you do FM with infinite feedback, the resulting wave would also have self-similarity.

[Big Gnome]

if you do FM with infinite feedback, the resulting wave would also have self-similarity.

...resulting in white noise, or something very, very similar.

[ItsMeOnly]

if you do FM with infinite feedback, the resulting wave would also have self-similarity.

...resulting in white noise, or something very, very similar.

You are thinking of DX-style FM, in reality you'll get razor sharp high pitched metallic tone.

[Sir Nose]

Some example fractal graphs and the resultant waveform
Fractal

Waveform that results from summing the above. If the nesting was continued to infinity the amplitude at the end would be infinite(it is the harmonic series).


Shifting the nesting to the left side of the waveform

The Sum


Nesting back at the right side of the waveform but using the sequence of triangular numbers to set the decay instead of the integers as above. This produces a finite value for the amplitude at the end of the waveform.

Sum, if continued to infinity the amplitude would have a value of 2 at the end of the waveform


Triangular Number decay nested on the left side

Sum

[Sir Nose]

More examples this time with sine waves.

Left-side Powers of 2 decay. (Right side is similar due to symmetry)

Sum


Sine waves with the nesting occuring at the center

Sum


Same as previous with every other sine wave inverted

Sum

[nogginj]

^^ beautiful

gracias