strange attractors, which means (in practice) they’ll create sequences that repeat.
not really… i apologise because i think my post in the other thread was too sloppy and misleading.
an orbit is a path that the system takes, where once you reach a point on that path you won’t leave it. it doesn’t need to be periodic. a rocket blasting into orbit, and thence remaining in orbit, is a fine example, but in this technical sense “falling off a cliff” is also an orbit.
most definitions of “chaos” specify that the system in question contains many periodic orbits of different lengths, that densely occupy the phase space.
attractors are sets of orbits that many different points in phase space will converge on.
strange attractors are when two or more attractors are sort of “interwoven” and its hard to predict whether a given point will go towards one or another of them.
any more specific definition of attractors quickly gets technical, even contentious. you would start by saying they are something like *limit sets that collect trajectories."
speaking to the OP, i think balance is good. it is very rare that i feel the need to deploy a hardware or software module whose specific purpose is to produce pseudorandom variables at the time scale of musical parameters. (even dear old darlings like the 266 SOU or
LFNoise2.kr.) i heave a little mental sigh when i see or hear the evidently scattered deployment of
[random] or slow CV pink noise. i often think that randomness is appropriate for “personal patching” but too often acts as a placeholder that never gets replaced.
(of course, at the audio time scale the situation is different, when we start perceiving probabilistic distributions as timbres instead of sequences of events.)
and on the other hand, sometimes of course aleatoric and stochastic processes are used in a very considered way to beautiful effect.
complexity exists everywhere and most especially in events that are taken from the material world - whether they are sampled audio sequences, spectral characteristics or the timing of a button press.
i think i end up frequently using processes that magnify that kind of complexity.
sometimes i think of musical traditions as lying a continuum of how they handle real-world complexity (aka randomness.)
- at one extreme there is sequenced music that is absolutely deterministic from every standpoint - the composition produces the sound wave, to the technical limits of fidelity
- there is the “score+performer” tradition, which locates indeterminism in the personality of the player and confines it within stylistic parameters.
- and of course there is a rich avant-garde tradition of exploring the limits and liminalities of the “score” paradigm, one of the most famous and fascinating is the cage+tudor partnership
- there are un-notated traditions, which are perhaps more porous to the influence of historical time (gamelan, rock and roll)
- there is structured improvisation and “free improvisation” and the various strategies to impose or destroy order in those spaces
- and there is field recording, the “direct” experience or “transcription” or “sonification” of natural processes.
i dunno, i guess it’s a big question, in terms of the poetics of structured sound. i think personally i enjoy using all of those approaches at various times, somtimes in direct juxtaposition.
and let me just point out: cage didn’t just throw the I ching once for ‘music of changes’ and send the results right off to peters to be published. he did it many times and picked results that he liked, using his brain as a filter for beauty. and he happened to be incredibly well attuned to beauty in music i think.
there is also building up complexity in a purely numerical space. like @rick_monster was saying about these sort of pseudo-Euclidean or LCG structures.
like in the design of the buchla 251e (quad sequencer) we made a bunch of funny decisions to amplify this kind of complexity:
- sequences can arbitrarily reset each others stages from arbitrary points, and be running on different time-bases.
- a seqeunce has begin and loop points. both of them can have counters (so after using a loop point N times, it will be ignored once, then the counter resets.) you can have nested loop points, each with their separate start/end counters. this can stay in the realm of sanity or quickly strain it.
- stage durations are arbitrary rational numbers.
don was interested in complex sequencing right from the start of buchla modular design. most of his sequencers had some kind of arbitrary jump / address ability. in feedback this gives you organic pseudo-randomness very quickly. (and the SOU modules through the 70’s are shift-register implementations of LCPRNG kinda algorithms, which are, haha, not very random at all - the sequences can be quite short.)
other design decisions are also telling: a function generator includes S+H. envelope followers are importnant. following a live signal into S+H into sequence position gives extremely complex behavior that still is performer-driven; technically it is quite simple and doesn’t require the explicit generation of pseudorandomness in the machine.
last night (making Halloween porch soundscapes) i revisited a funny firmware from 200e. for the wavetable oscillator we made a variant where the tables in one bank are just different offsets into the flash memory (including preset memory,) and when these tables are selected the input for FM index becomes an offset scrubber. it’s a fun one because the parameterization of the sound remains the same, and learned control gestures apply, but the acoustic terrain that you’re actually controlling is suddenly alien and unknowable. (and frequently capable of great beauty and expressiveness, i find)