Ian Fritz MegaCycler demo with O'Tool

Published on Jan 5, 2013 frijitz001·8 videos

Demonstration of MegaCycler triggeringing synth events viewed with Dave Jones' O'Tool "oscilloscope. Refer to this thread http://electro-music.com/forum/viewtopic.php?highlight=billiard+chaos&t=41115"


"So ... if you feed two Tri waves into your scope and look at the xy display (Lisajou figure) you see what looks like a ball bouncing around a billiard table. This makes sense, because the ball has constant speed in the x and y directions corresponding to the constant positive and negative slopes of the two waves.

In mathematical dynamics there is a class of problems called "billiards" related to billiard balls bouncing around tables (which may have a variety of shapes). The tables may also have objects placed on them (again, with a variety of shapes), so the ball bounces off both the table boundaries and these objects.

These billiard trajectories have unusual and interesting properties. For example, a square table with a square obstacle aligned with the table has some trajectories that are periodic (i.e., retrace themselves repeatedly), or quasiperiodic, and some that are highly irregular. The irregularity is often called "pseudo chaos", meaning that it seems as irregular as in chaotic systems, although the system does not satisfy the usual mathematical criteria for chaos.

Getting back to the two Tri oscillators, it is quite easy to electronically simulate an object on the table by using a bunch of comparators and a means of reversing the direction of the oscillators at any time. A familiar oscillator is the Tri VCO based on comparators and an RS flip-flop, such as in the Electronotes TZFM VCO that a number of folks here have built.

So I set up circuit like this, with trajectories modified when the "ball" is in certain regions. (These are not true physical reflections, but never mind, the idea is the same.) Here are some results:

Figure 1 is a scope shot of a trajectory that is periodic, with many trips around the system before repeating. Figure 2 is a photo of a nearby trajectory that shows the irregular behavior of pseudo chaos. This is seen in the areas that look like bands, where the trajectories densely fill the areas.

Figures 3 and 4 show the frequency spectra of the two trajectories. The pseudo chaotic one has a broad and quite strong background feature, just like seen in spectra of the more familiar chaotic systems. The periodic one has many strong overtones.

Finally, the mp3 has two sections, corresponding to the photos, so you can hear what pseudo chaos sounds like.

I'll try to post some more examples later, if anyone is interested.

Ian

Edit: Computer simulations seem to indicate that the trajectories in this system are periodic, often with many thousands of bounces per period. The irregularities seen above are probably related to noise in the system modulating the path in a discontinuous manner. Still pretty interesting, though!"