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 Forum index » Clavia Nord Modular » G2 Patches - Experimental
A Chaotic LFO
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jamos



Joined: Jun 01, 2004
Posts: 470
Location: Eugene, Oregon, USA
Audio files: 4
G2 patch files: 36

PostPosted: Sat Jan 15, 2005 11:49 am    Post subject: A Chaotic LFO Reply with quote  Mark this post and the followings unread

This simple patch implements the "logistic equation", which is a simple way to generate non-repeating, chaotic patterns.

Adjust the knob labeled "3 < k < 4" to vary the pattern from ordered to random.


Chaos Generator.pch2
 Description:
Implements the chaotic "logistic equation".

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 Filename:  Chaos Generator.pch2
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Last edited by jamos on Mon Jan 17, 2005 9:25 pm; edited 2 times in total
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cebec



Joined: Apr 19, 2004
Posts: 1066
Location: Virginia
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PostPosted: Sat Jan 15, 2005 9:41 pm    Post subject: Reply with quote  Mark this post and the followings unread

cool, thanks for this...
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zynthetix



Joined: Jun 12, 2003
Posts: 838
Location: nyc
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G2 patch files: 13

PostPosted: Sun Jan 16, 2005 12:55 pm    Post subject: Reply with quote  Mark this post and the followings unread

Thanks much for this patch. I have not tried implementing logistic EQ on the G2, but I did some work with it in reaktor. you might find the attatched audio clip of interest:


gxaos1.mp3
 Description:
recording of reaktor noodle: 4 logistic eq's, each with different constants and their own sampler. The same sample is being triggered in all 4, two strums of a dom7 chord on an acoustic guitar. The eq's are also set up to cross modulate the pitches, st

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 Filename:  gxaos1.mp3
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jamos



Joined: Jun 01, 2004
Posts: 470
Location: Eugene, Oregon, USA
Audio files: 4
G2 patch files: 36

PostPosted: Mon Jan 17, 2005 9:27 pm    Post subject: Reply with quote  Mark this post and the followings unread

Thanks, fellers.

I figured out how to fix the annoying reset behavior, and it even requires fewer modules. The new version is up.
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ian-s



Joined: Apr 01, 2004
Posts: 2585
Location: Auckland, New Zealand
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PostPosted: Mon Jan 17, 2005 11:32 pm    Post subject: Reply with quote  Mark this post and the followings unread

This is great.
The output also makes some interesting, organic tones if clocked by an oscD.

Thanks for posting
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mosc
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Joined: Jan 31, 2003
Posts: 17630
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PostPosted: Tue Jan 18, 2005 7:43 am    Post subject: Reply with quote  Mark this post and the followings unread

I love this. Didn't know about it before. Thanks much...

Zynth, your track sounds fab. Cool

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egw



Joined: Feb 01, 2003
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PostPosted: Tue Jan 18, 2005 8:53 am    Post subject: Reply with quote  Mark this post and the followings unread

Could you post the equation here, or a pointer to a site that explains it?
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jamos



Joined: Jun 01, 2004
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PostPosted: Tue Jan 18, 2005 11:10 am    Post subject: Reply with quote  Mark this post and the followings unread

egw wrote:
Could you post the equation here, or a pointer to a site that explains it?


The equation is

x[t+1] = k * x[t] * (1-x[t])

If you Google on "chaos" and "logistic equation", you'll find far more explanations than you can possibly read :') A good one is at http://hypertextbook.com/chaos/42.shtml .
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egw



Joined: Feb 01, 2003
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PostPosted: Tue Jan 18, 2005 2:48 pm    Post subject: Reply with quote  Mark this post and the followings unread

How do you know that k should be between 3 and 4?
Trial and error, or is it a recommended value?
Are there any constraints on x[0] besides not equal to 0?
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jamos



Joined: Jun 01, 2004
Posts: 470
Location: Eugene, Oregon, USA
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G2 patch files: 36

PostPosted: Tue Jan 18, 2005 4:00 pm    Post subject: Reply with quote  Mark this post and the followings unread

egw wrote:
How do you know that k should be between 3 and 4?
Trial and error, or is it a recommended value?
Are there any constraints on x[0] besides not equal to 0?


Mostly 'cause I'm taking a class in chaos theory and know all this shit real good Very Happy

But the way you can really tell is from that bifurcation diagram at the bottom of the page that I referenced. This shows that for values of k (they call it r) < 3, the attractor is a fixed point - DC, in other words. No good. Even for k < ~3.57, the output is not chaotic, or even interesting - just two values (a square wave).

X[0] has to be between 0 and 1, exclusive. If it's either of those the output will go to 0. If it's greater than 1, the function goes to infinity. In G2 terms, 1 == 64; that took a while to figure out (look at the docs on the level multiplier, that's where I picked up the relevant tidbit.) The result is that the output (the green cords) swings from 0 to +64.
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mosc
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Joined: Jan 31, 2003
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PostPosted: Tue Jan 18, 2005 8:52 pm    Post subject: Reply with quote  Mark this post and the followings unread

Zynth, now that you can see how to make this chaos patch using the G2, why not try a version of the Reaktor patch and let us see how it's done? This stuff if facinating.
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