Billiard-Dynamic Pseudo Chaos Generator

6079smith · Posted: Wed Apr 14, 2010 5:45 am Post subject:

Those two demos are brilliant. Just thought I'd say that.

bridechamber · Joined: Oct 06, 2007 Posts: 64 Location: Saint Paul, MN

Did I already say "Drool...."?

I'm going to need a bunch of these!
The first sample sounds somewhere between brass and woodwind. What a lot of tonal range between just those two samples!

frijitz · Posted: Thu Apr 15, 2010 12:42 pm Post subject:

Thank you Scott and smith for the kind words. Making demos is a real challenge for me.

Right now I'm wrestling with the question of how people would be able to use this toy without hooking it up to a scope. scratch

I am in the process of adding gate and trigger outputs to delimit the times when the ramps are going either up or down (gates) and when they are starting and stopping (triggers). Maybe these could be used to light LEDs (or something).

Very Happy

Ian

Dan Lavin · Posted: Thu Apr 15, 2010 12:54 pm Post subject:

Ian,

Would one of these help? I think these have been mentioned on a thread or two when they were first introduced. But at the time I couldn't think of an application where a regular oscilliscope wouldn't be a better choice.
http://www.gearfuse.com/diy-oscilloscope-kit/

blue hell · Posted: Thu Apr 15, 2010 1:25 pm Post subject:

TekniK · Joined: Aug 10, 2008 Posts: 1059

frijitz · Posted: Thu Apr 15, 2010 2:18 pm Post subject:

Dan Lavin · Posted: Thu Apr 15, 2010 7:31 pm Post subject:

Ian:
I ordered one earlier this week that is supposed to be delivered tomorrow. It was $35 with the smd parts presoldered (doesn't leave that much for me, does it?). I'll be fooling with it on the bench for a few weeks, but if I notice anything funky, I'll let you know. I was hoping this would help out. Most of the times I rule these things out for being single channel or low frequency, but your application could be ideal for it, You can still get a pretty descent module with your base circuit plus this for not a whole lot of money and there seem to be a large number of distributors selling the things.

frijitz · Posted: Tue Apr 20, 2010 11:02 am Post subject:

Here are some more demos.

The first uses slow sweeps similar to the previous two clips. One of the "pillar" heights is being changed slowly by hand.

In the second clip the frequency of one of the oscillators is being changed very slowly, again manually.

Very Happy

Ian

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andrewF · Posted: Wed Apr 21, 2010 2:19 am Post subject:

they both sound really good, definitely musical.
am looking forward to seeing how this design ends up

frijitz · Posted: Wed Sep 22, 2010 2:37 pm Post subject:

There hasn't been much time to work on this project over the summer, but there's more free time now to move it ahead. I rebuilt the system on perfboard, with the two oscillators totally separate to avoid some syncing that was happening at certain frequency ratios. The current sources were changed from linear to exponential to make tuning at the low end easier. The window comparator circuits were made with opamps rather than the bargraph display originally used. Circuitry to derive gate and trigger signals from the various collisions has been developed and is half built.

Here's a new demo. The collisions with the two y-axis boundaries produce triggers which fire S/H's sampling the two oscillator outs. These triggers and voltages control a pair of VCO/VCF/VCA patches. The VCFs are a pair of Threelers set to operate in the regime above self oscillation. This gives a wide variety of sounds that change with every reflection.

The system is cyclic with a period of about 20 loops around the table. The time for one repetion is about 23 sec, which you should be able to hear.

Very Happy

Ian

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The Bad Producer · Joined: Mar 08, 2009 Posts: 282 Location: The Manhole

Wow, I'd forgotten about this...

Amazing! Quite beautiful...

Very Happy

andrewF · Posted: Wed Sep 22, 2010 5:23 pm Post subject:

Very beautiful!!
This is what inspires me to learn more about chaos.
Thanks Ian

frijitz · Posted: Fri Oct 01, 2010 9:04 pm Post subject:

Here is some more information on the workings of the MegaCycler. Imagine a square, ideal billiard table (no friction, no pockets, perfect collisions). When you set the ball off in an arbitrary direction its trajectory will eventually cover the whole table uniformly. Now put an object on the table and the story is totally different. In the MegaCycler the objects are rectangular areas, but when the ball hits an object it isn't actually reflected, as a real ball would be. Instead, when the ball hits the boundary of an object from the outside, all that happens is that the velocity in one of the directions is reversed. Nothing happens when the ball leaves the object. This sounds kind of crazy, but it seems like the simplest rule that can be easily implemented with analog electronic circuits. And the results are amazing!

The drawing shows a typical fairly simple trajectory, obtained by computer simulation. The table is the unit square, and the ball reflects off of the four rails in the expected manner. In the circuit, these reflections are the normal reversals of the triangle-wave oscillators. The object is represented by the blue rectangle. The position and height of the object are variable. There is also a second object (not used in this example) anchored to the vertical axis. In the electronic implementation, a set of comparators define the boundaries of the object. As soon as the object is entered a trigger signal reverses the direction of one of the oscillators. It would be possible to implement actual reflections at the object boundaries, but quite a bit more work.

Imagine the ball being launched from the position of the red dot at an angle slightly larger than 45 deg. Its path is indicated by the arrows. When the ball hits the object it reverses in the y direction. It then bounces off the four walls before hitting the object again, once more reversing in the y direction. Four more bounces off the walls and it arrives back at its starting point. What! Yes, the ball stays on the same path forever. It can easily be shown with a bit of geometry and trig that the path is indeed closed as shown. In fact the initial launch point and velocity can be changed some and the path will still be closed. All that is necessary is that the ball hits all the boundaries in the same sequence.

In the computer simulations the paths are always closed. However it may take many circuits around the table for this to happen. One case I pursued a bit took over 100,000 collisions before repeating! In the circuit, noise and drift make it impossible to see such long periods. But I can see some that seem to take over several hundred collisions to repeat.

Gate and trigger circuits have now been added for each leg of the trajectory. The mp3 comes from a pattern with 12 collisions. Some of them are used to trigger three voices. Very simple, but it shows that you can get interesting regular rhythms out of the system.

Very Happy

Ian

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frijitz · Posted: Sun Oct 03, 2010 5:35 pm Post subject:

So here's a photo of the MegaCycler prototype as of now. I'm going to leave it as is for a while while I play with it some more, to decide whether the current parameter set is sufficient or if anything doesn't make sense to keep.

The upper board carries the two VCOs (the two columns on the right), the two expo converters, some signal scaling and the gate and trigger circuits. The lower board has the comparators to detect when the ball enters each object and trigger signals for those events.

The left side of the panel has controls for the oscillator frequencies and to define the position and height of the two objects. An FM input for the y direction has been incorporated. To the right of the FM control are the two trigger signals that signal when ball hits the object. On the right are all the main VCO outputs: the x and y signals, a gate signal for the upramp phase of either wave, along with triggers signaling the beginnings of the upramp and downramp segnents.

Very Happy

Ian

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Sound · Joined: Jun 06, 2006 Posts: 842 Audio files: 1

This project looks very interesting, I would be interested in a PCB. Thanks. Very Happy

TekniK · Joined: Aug 10, 2008 Posts: 1059

Realy nice Ian.

frijitz · Posted: Sat Oct 09, 2010 12:46 pm Post subject:

Here's another demo of the MegaCycler. The patch is based on a Teezer VCO slaved to a second VCO using a sync level near midpoint. The Teezer's linear FM input is swept continuously by the output of the y-axis signal of the MegaCycler. You can hear a bit of crunchies as the sync locks in.

The FM of the master VCO is controlled by the x-axis signal of the MegaCycler, sampled at one of the y-axis slope reversals. The x-axis gate and trigger control an ADSR giving the overall amplitude envelope.

The y-axis oscillator is FM'ed by a square-wave LFO, cycling every 30 seconds or so. So there are two different paterns controlling the patch. The slower one tends towards a fixed orbit, but usually doesn't make it all the way there. An exception is at 1:30 in the clip, where you hear the periodic pattern.

Very Happy

Ian

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ehdyn · Joined: Sep 13, 2007 Posts: 33 Location: Caerdydd, Palau

Any chance for moving walls?

If you throw in a moat and windmill you can call it the Putt-Putt