Hey I have been reading a lot about chaos equations and the like recently. I found interesting analog chaos computers and have seen some chaos equations that can be fed an input such as an oscillator or audio stream and output a very interesting and complex output.

Anyway I am a little lacking in the differential calculus skills and I am having troubles inputting equations with t) type things into an fexpr~ or expr~. I did see the lorenz attractor example in the help for expr~, but if someone could help me figure out how to get from a differential equation to an expr~ or fexpr~ that calculates it that would be awesome. Or maybe I just need to get some calculus books.

the page below has some examples of the types of equations I am talking about.
http://www.viewsfromscience.com/documents/webpages/chaos.html

Thanks

So I am not sure if the problem I am having is a technical limitation of PD or if I am calculating something wrong.

I figured out I could add two square waves, one twice the frequency and half the amplitude to get a sawtooth wave. but it doesn't work.

I know there is a phasor~ object to get a sawtooth, just trying to figure something out before I try it in hardware.

if a square has odd harmonics I think at the same ratio as a saw has it's even harmonics then why can't I add two squares, one that is the base freq for all my odd harmonics and one that is X2 freq and half amplitude to get all of my even harmonics?

forgot to say I tried this in pd and I get something that sounds a lot like a sawtooth, but graphed out looks like a 3 step ladder sawtooth instead of a smooth line going from 0 to 1.

I have been working a lot with PD lately and have built some synths that I think make some pretty interesting sounds. I have also built some sequencers that produce complex patterns.

I have lately been researching modular analogue sequencers, the big rack type things. This has been giving me ideas about building a complete modular system with PD.

I have been thinking I could use my synths and sequencers together much more easily if they were modular. Also if a modular standard was developed, like standard CV ranges in analogue gear, we could trade module patches back and forth and build huge systems.

I have a few things I have been trying to figure out.

• since this system is modular would I be better off with something with vst au rtas ladspa etc. support? like a daw with reaktor? I would be able to patch back and forth between the effects and sound generators.

• does anyone know a good way to run the output from a program like reason or a daw into PD on OSX? I can't figure out how to do it with jack. I have been running out to my sound card and then back into it with a patch cable(completely ridiculous)

• it appears there will always be some type of delay/lag/buffer/latency with PD, maybe with all software synths? In my masterplan giant modular system with a computer and some external analogue effects / sound generators I could patch out of the computer and then back into it. Will the latency kill me doing this? will a crazy quad core tons of ram computer deal with super low latency?

I know that is a bunch of questions in one post, but if anyone has any ideas let me know.

Thanks

in OSX you can also use the system monitor, it is in apps/utilities to see how much cpu PD is using. A way to see if the gui is what is killing you is to watch how the system monitor changes when you minimize a patch. On my quad core i5 I saw the cpu go from 70% down to 3% when i minimized a patch, so that gives you an idea of how inefficient the gui is, this is with the audio still running, so 3% of cpu for sound 67% for gui. I have since then started making my guis more sparse.

So I added some different ways of scaling the number from a 0 to 1 range to a frequency range. Some of them sound cool, but they don't really change the fact that the high end of the frequency range seems more prevalent than the low end. I came up with the idea based on the 1 volt per octave idea in analogue modulars, if you had a linear frequency response most of the knob range would be high piercing sounds, but with a 1 volt per octave range you get way more range in the bottom end.

I think the reason this patch sounds higher pitched though is just because the higher frequencies of filtered noise seem louder. Maybe using pink noise or having the volume scale down as the pitch scales up would fix this. I didn't have time to try those out yet.

thanks for the iteration info JensChr I will research that some.

http://www.pdpatchrepo.info/hurleur/chaosFilteredNoise2.pd

ok here is something I made using the calculation. It makes some patterns I think are kind of interesting. Also some of them seem repetitive at first, but if you listen for a while you will hear variations. I am kind of surprised how repetitive it is. I would think it would be a little more random sounding.

Sorry I didn't get anything up sooner, I got distracted editing a film for a friend.

http://www.pdpatchrepo.info/hurleur/chaosFilteredNoise.pd

Yes, I was joking about having someone else make a C external for me, unless it is something they are interested in as well. Also looking at the patch that katja made I realized it might be a little simpler than I thought to get the equations into fexpr~

So I just need to study up on my calculus now.

oh also what does [click~] do? there is no help for it.

ok thanks for that patch, I was playing around with it and it clarifies a few things. Seeing the equation and then the patch helped me out. So what I need to figure out is how to do the integration part. Which is calculus?

As far as the difference between chaos equations and random number routines. I think sometimes complex chaos equations are used for pseudo random numbers, but like the first quote says on the view from science page chaos systems are deterministic and non-linear.

My idea for implementing chaos equations musically was mostly to use them as controls for creating not quite random patterns that are hopefully interesting. But I also like the way they sound as an alternative to noise or for generating complex waveforms.

Another idea I had was to get ideas of what equations are interesting and somehow use those equations as inspiration for slightly less complex equations which would create less random but somewhat chaotic controls.

The link didn't work, so i'm not sure what type of netbook it was, but I did install PD on a friends netbook running ubuntu and it worked fine. His netbook was a samsung n10. It had an atom chip in it.

Well it seems there are multiple people who would like to be able to get these equations into PDable formats, I wonder if we could find someone with an understanding of C and an understanding of differential calculus who could make an external that you would just type in the equation and PD would calculate it. maybe that is a little wishful thinking.

you could also samphold~ or unsig~ or snapshot~ a noise~ which is random and goes from -1 to 1, those might be slightly more cpu heavy though.

ok that makes sense.

The reason I was trying to figure out how to put squares of together to make a saw was because I was trying to figure out how to do it with cheap hardware that only produces square waves (555 timers, 40106 switches) combined with a multiplexor/divider chip.

as for pulses in PD I like.

[phasor~] [0-1]
| |
[fexpr~ $x1 > $x2]

the 0-1 adjusts the PW.

thanks

Awesome, thanks for the jackosx help.

plugin support would be helpful because say I have a plugin that is a really good filter or distortion etc. etc. yes I could build something in PD that would be equivalent, but I guess the whole point of what I am thinking of is to have options open to use almost any hardware or software sound devices together. Although on the other hand maybe I will learn more if I try to emulate the plugins I would use in PD instead of integrating the plugins themselves into my modular system.

As far as standards go I guess I was thinking more that patches for the modular system be designed not just as a standalone item (although some could be used standalone as well) but to be able to be opened inside of another patch with inlets and outlets for controlling the parameters and inputting and outputting sound.

Thanks for the recommendation of the diy2 library I will check it out.