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 Forum index » Clavia Nord Modular » G2 Building Blocks
True chaos generator
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Rob



Joined: Mar 29, 2004
Posts: 580
Location: The Hague/Netherlands/EC
G2 patch files: 109

PostPosted: Wed May 25, 2005 4:53 pm    Post subject: True chaos generator Reply with quote  Mark this post and the followings unread

Here is a chaos generator with bifurcations, strange attractors, et all. It creates either a stepped or a smoothly gliding chaotic signal. Chaotic means it creates repeating 'random' patterns. When switching from one pattern to another there will be a short random transition until it hangs in a new repeating pattern. This transition can be heard when e.g. changing variations or changing the bank or pattern knobs. Basically each pattern is a strange attractor.

At the core is a PM oscillator set to 0 Hz, acting as the non-linear component in the chaotic but deterministic system. A constant value is added to its output and then fed back through a sample and hold to its PM input. So the chaos function is simply: x'=2*Pi*sin(x)+A.
An eight output clocked delay is used as a S&H array. The 'S&H delay' is clocked by a sawwave and this same sawwave is used to crossfade between two adjacent outputs of the clocked delay. This creates a total of seven smooth linear glides that lag each other, to form sort of a canon of glides. And eight step values that also lag one step.

Posted Image, might have been reduced in size. Click Image to view fullscreen.

The Bank and Pattern constants define the pattern and there are over 16000 patterns in this patch, but theoretically there are millions. Any smoothed glide output can be used to modulate the rate of the S&H clock, to create a sense of acceleration and deceleration.

The thing is driven by a lfo module set to a sawwave and can be running as fast as some five octaves above 165 Hz. The lfo is used as the sawtooth is not anti-aliased, which helps to prevent gliches in the smoothed glides. The anti-aliasing on a red sawtooth would actually create a glitch.

Not much more to say about this particular patch than that the vocoders just give a nice round sound to the modulated triangle waves that are controlled by the glides.


SmoothedChaos.pch2
 Description:
A pattern generator that creates smooth linear glides according to the rules of Chaos Theory. Read the book Chaos by James Gleick to read in on the subject.

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 Filename:  SmoothedChaos.pch2
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Jason



Joined: Aug 12, 2004
Posts: 466
Location: Los Angeles, CA. USA

PostPosted: Wed May 25, 2005 5:05 pm    Post subject: Reply with quote  Mark this post and the followings unread

Very nice!
In fact ... Awesome! Surprised
I just wish I could understand a bit more of what its doing , I am just getting familar with the G2 still.
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ian-s



Joined: Apr 01, 2004
Posts: 2575
Location: Auckland, New Zealand
Audio files: 42
G2 patch files: 608

PostPosted: Wed May 25, 2005 5:58 pm    Post subject: Reply with quote  Mark this post and the followings unread

strange, and attractive. Very Happy
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jksuperstar



Joined: Aug 20, 2004
Posts: 2488
Location: Denver
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PostPosted: Wed May 25, 2005 6:21 pm    Post subject: Reply with quote  Mark this post and the followings unread

Several years ago, there was a "Scientific American" magazine article that showed using 2 identical "chaos" boards (analog w/opamps, etc) to modulate a voice signal. The intent being that you could use them to talk over the phone, with almost no chance of someone else "decoding" the messege. The article was later pulled, due to government pressure and "restrictions" on printing such schematics.

But, it seems we are back to full chaos....G2 in espionage anyone?
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Jason



Joined: Aug 12, 2004
Posts: 466
Location: Los Angeles, CA. USA

PostPosted: Wed May 25, 2005 6:41 pm    Post subject: Reply with quote  Mark this post and the followings unread

lol that is so fascinating actually, I am awful at math but find chaos theory and fractals just amazing, good story jksuperstar.
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Afro88



Joined: Jun 20, 2004
Posts: 701
Location: Brisbane, Australia
Audio files: 12
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PostPosted: Wed May 25, 2005 8:45 pm    Post subject: Reply with quote  Mark this post and the followings unread

Really cool, thanks Rob Smile

I think it sounds really nice on some pattern/bank combo's when the chaos gets caught up on itself and starts repeating a small slowly evolving section. Really nice.

Var 8, 6, 5 and 3 really agree with me Cool
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Rob



Joined: Mar 29, 2004
Posts: 580
Location: The Hague/Netherlands/EC
G2 patch files: 109

PostPosted: Thu May 26, 2005 2:32 am    Post subject: Re: True chaos generator Reply with quote  Mark this post and the followings unread

Rob wrote:
The Bank and Pattern constants define the pattern and there are over 16000 patterns in this patch, but theoretically there are millions. Any smoothed glide output can be used to modulate the rate of the S&H clock, to create a sense of acceleration and deceleration.


What I forgot to mention is that a pattern also depends on its initial state when the Bank and Pattern knob are changed. Meaning that a certain setting can actually produce several different patterns, and it is a surprise which one turns up. This is as a certain state can have several strange attractors as a property. This surprise factor is of course what Chaos is all about, the possible but not imminent generation of 'Happy Accidents'.

A little personal reflection on Chaos:
Mostly 'Accidents' are contributed to either a 'Freak of Nature' or the 'Will of God'. Curiously the happy ones are often attributed to Nature and the unhappy ones to God. Like when God created mankind, which is not too difficult to see as an unhappy accident, He immediately turned mankind itself into the manifestation of His repentence of His own mistake. Thank Him for that, you Creationists! Why didn't He use a couple of weeks, or months, or eon's, for doing His creation and do a better job?
Luckily I'm at the Naturalist side of things myself, where all is just one big Happy Accident and life is very good and where the number 42 says it all. Heiho!
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mosc
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Joined: Jan 31, 2003
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Location: Allentown, PA
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PostPosted: Fri May 27, 2005 2:23 pm    Post subject: Reply with quote  Mark this post and the followings unread

This chaos thing is confusing to me. Rob, please come by my house sometime this week and explain it to me. Thanks... Laughing
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Rob



Joined: Mar 29, 2004
Posts: 580
Location: The Hague/Netherlands/EC
G2 patch files: 109

PostPosted: Fri May 27, 2005 2:46 pm    Post subject: Reply with quote  Mark this post and the followings unread

mosc wrote:
This chaos thing is confusing to me. Rob, please come by my house sometime this week and explain it to me. Thanks... Laughing


Yeah, could do that. Somewhere in the middle of the week? You mind if I bring a friend? Smile
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mosc
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Joined: Jan 31, 2003
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G2 patch files: 60

PostPosted: Sat May 28, 2005 8:38 am    Post subject: Reply with quote  Mark this post and the followings unread

Laughing Joker and I are warming up the Moog Modular for you.
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G2egory



Joined: Nov 19, 2004
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Location: Charlottesville VA
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PostPosted: Sat May 28, 2005 10:16 am    Post subject: Re: True chaos generator Reply with quote  Mark this post and the followings unread

Positively wonderful patch. What a versatile building block. There is so much that you can modulate. I can't wait for my teenage son to play with it. Sometimes he comes up with coolest sounds.
Thanks for sharing.

Surprised Very Happy
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jofb



Joined: Jun 01, 2005
Posts: 6
Location: porto portugal
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PostPosted: Thu Jun 02, 2005 9:53 am    Post subject: Reply with quote  Mark this post and the followings unread

thanks a lot for sharing. i believe my picture is a representation of this. if someone is interested in knowing more about this visit http://mathworld.wolfram.com/LogisticMap.html
best regards jofb

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jamos



Joined: Jun 01, 2004
Posts: 470
Location: Eugene, Oregon, USA
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PostPosted: Thu Jun 02, 2005 10:45 am    Post subject: Reply with quote  Mark this post and the followings unread

The chaos function here uses a sine function rather than the logistic map, which probably results in more musical patterns (I think, haven't tried this one yet). The chaos generator I did previously (which is also a true chaos generator Razz) uses the logistic equation; see http://www.electro-music.com/forum/topic-4823.html
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jofb



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PostPosted: Thu Jun 02, 2005 11:07 am    Post subject: Reply with quote  Mark this post and the followings unread

scratch have to check it better. thanks thumleft
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ian-s



Joined: Apr 01, 2004
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PostPosted: Thu Jun 02, 2005 1:04 pm    Post subject: Reply with quote  Mark this post and the followings unread

I don’t know a lot about chaos theory, but I have plenty of experience with chaos in practice. Just try supermarket shopping with 4 kids under 6.

Shocked Very Happy
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jofb



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PostPosted: Thu Jun 02, 2005 1:57 pm    Post subject: Reply with quote  Mark this post and the followings unread

Very Happy well g2ian! if eatch one of the kids goes his seperat way your experiencing chaos Shocked why not think modular and put some cables on them so they behave as one Laughing cheers
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jksuperstar



Joined: Aug 20, 2004
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PostPosted: Thu Jun 02, 2005 2:24 pm    Post subject: Reply with quote  Mark this post and the followings unread

Ian - would you consider yourself to be an attractor then? Funny how "Attractor" differs between single & married life, eh?
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Rob



Joined: Mar 29, 2004
Posts: 580
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PostPosted: Mon Jun 13, 2005 8:05 am    Post subject: Reply with quote  Mark this post and the followings unread

jamos wrote:
The chaos function here uses a sine function rather than the logistic map, which probably results in more musical patterns (I think, haven't tried this one yet). The chaos generator I did previously (which is also a true chaos generator Razz) uses the logistic equation; see http://www.electro-music.com/forum/topic-4823.html


Yeah, basically every non-linear function is potentially chaotic. The sine has the advantage that it produces nicely distributed numbers between minus and plus one, symmetrically distributed around zero. Which is musically of more use than e.g. the common x'= 4x (1-x).

My reference to 'true' chaos was only to differentiate it to e.g. Buchla's Source of Uncertainty and the Wogglebug, etc. As those are not really exhibiting the bifurcations thingies, etc., and so imho do not really classify as chaos generators but more as common random generators. But of course this is not that important, as all are fun.
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ian-s



Joined: Apr 01, 2004
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Location: Auckland, New Zealand
Audio files: 42
G2 patch files: 608

PostPosted: Thu Jun 16, 2005 7:59 pm    Post subject: Reply with quote  Mark this post and the followings unread

Rob wrote:
My reference to 'true' chaos was only to differentiate it to e.g. Buchla's Source of Uncertainty and the Wogglebug, etc. As those are not really exhibiting the bifurcations thingies, etc., and so imho do not really classify as chaos generators but more as common random generators. But of course this is not that important, as all are fun.


Actually the #3 Wogglebug is an interesting circuit.

http://www.musicsynthesizer.com/WoggleBug/WoggleBug.html

It is descended from Buchla’s design but instead of sampling and filtering a noisy triangle, the smooth cv controls a VCO who’s sawtooth output becomes the input to the sample & hold. The author describes this as recursive but I would just call it feedback. Anyway like Rob said, a lot of fun. The correlation function on these SOU modules seems equivalent to the Step control on the NM random group, reducing the range of consecutive output samples by ‘recursively Rolling Eyes ’ sampling your own output.
I built a G2 woggle patch but unfortunately, the Type 2 phase comparator works a little too well and refuses to woggle much at all. The PLL might come in useful later though.
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cappy2112



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PostPosted: Thu Jun 16, 2005 10:10 pm    Post subject: Reply with quote  Mark this post and the followings unread

jksuperstar wrote:
Several years ago, there was a "Scientific American" magazine article that showed using 2 identical "chaos" boards (analog w/opamps, etc) to modulate a voice signal. The intent being that you could use them to talk over the phone, with almost no chance of someone else "decoding" the messege. The article was later pulled, due to government pressure and "restrictions" on printing such schematics.

But, it seems we are back to full chaos....G2 in espionage anyone?


Well, there are 4 audio inputs.....
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