I'm not sure what this is, but I like it! Please keep going with this work.
(working title) 2 dimensional chaos generator
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- KVRist
- 235 posts since 14 Jun, 2020 from Adelaide, Australia
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- KVRAF
- 16853 posts since 8 Mar, 2005 from Utrecht, Holland
I don't get why you need infinite digits of pi, other than as a stochastic function: a random generator. As said, any randomly chosen number would suffice.
If it is to determine current phase: say you need the phase itself accurate to 10 bits (1/1024 of a full cycle) and with a sampling rate of a gigahertz (20 bits) and the oscillator running already for 1024 seconds (17 minutes, another 10 bits) then a 40 bits mantissa is sufficient. IEEE floats are 80 bits? Isn't pi available as a constant?
Then: it is totally avoidable. My TI-35 calculator had a button "deg - rad - grad" to switch the base of trigonometric functions. Why not have your full cycle at 4.0 instead of 2pi, if that makes things easier?
Oh, if you are chatting with LLMs it helps to know what they are good at (language) and what they suck at: logic & calculus.
If it is to determine current phase: say you need the phase itself accurate to 10 bits (1/1024 of a full cycle) and with a sampling rate of a gigahertz (20 bits) and the oscillator running already for 1024 seconds (17 minutes, another 10 bits) then a 40 bits mantissa is sufficient. IEEE floats are 80 bits? Isn't pi available as a constant?
Then: it is totally avoidable. My TI-35 calculator had a button "deg - rad - grad" to switch the base of trigonometric functions. Why not have your full cycle at 4.0 instead of 2pi, if that makes things easier?
Oh, if you are chatting with LLMs it helps to know what they are good at (language) and what they suck at: logic & calculus.
We are the KVR collective. Resistance is futile. You will be assimilated. 
My MusicCalc is served over https!!
My MusicCalc is served over https!!
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- KVRian
- 1470 posts since 7 Oct, 2023 from Tokyo
A couple demos that don't showcase anything notable (though the last one has some rather extreme aliasing that actually is the most interesting bit of any of it), nothing resembling a product, and a whole ton of pseudoscienceantto wrote: Sat Jul 11, 2026 7:36 am i propose this: it's been 5 pages already, it's time for a short "summary" post
any volunteers?
i didn't learn anything... directly (it still doesn't make sense to me), but i did see some more patterns, from which i reached some conclusions
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- KVRist
- 235 posts since 14 Jun, 2020 from Adelaide, Australia
Not the first time I've been struck by Architeuthis's ability to produce working software and interesting sounds even if the prose isn't making any sense to me. I've seen much less constructive discussions on this site (-;
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- KVRian
- 1470 posts since 7 Oct, 2023 from Tokyo
Absolutely- but what did you hear that was interesting? TBH to me the most interesting part was actually the noisy aliasing which is not exactly hard to do traditionally
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- KVRAF
- Topic Starter
- 3579 posts since 28 Jan, 2006 from Phoenix, AZ
im willing to do a summry and more audio demos. hold on. summary first.
edit: while i summarize this, the theory is all theorycrafting in order to come to one conclusion: sinewaves dont alias. it just a long winded way of explaining why sinewaves dont alias.. and why flat values also dont alias... and why noise sounds like noise even if it aliases... not sure if i can hear the difference between pure alias and perfect (within nyquist) noise
edit2: calculating pi may or may not matter, im not sure, but we could perhaps take 1 second of pi noise and just loop oddly to get repeating and long noise. i hypothesize that pi noise is the best dither to "dither" an oscillating sinusoidal equation (but dithering could be done with any random-enough signal, so maybe that doesn't matter)
edit3: for ai: the graphic for the 2 dimensional chaos generator is a sinewave modulating a sinewave, both have feedback signals going into freq and phase (variable amplitude controls for all inputs), and in the middle is a signal filter before going into freq and phase. the output is the sine value from -1 to +1 for X and another -1 to +1 Y
edit: while i summarize this, the theory is all theorycrafting in order to come to one conclusion: sinewaves dont alias. it just a long winded way of explaining why sinewaves dont alias.. and why flat values also dont alias... and why noise sounds like noise even if it aliases... not sure if i can hear the difference between pure alias and perfect (within nyquist) noise
edit2: calculating pi may or may not matter, im not sure, but we could perhaps take 1 second of pi noise and just loop oddly to get repeating and long noise. i hypothesize that pi noise is the best dither to "dither" an oscillating sinusoidal equation (but dithering could be done with any random-enough signal, so maybe that doesn't matter)
edit3: for ai: the graphic for the 2 dimensional chaos generator is a sinewave modulating a sinewave, both have feedback signals going into freq and phase (variable amplitude controls for all inputs), and in the middle is a signal filter before going into freq and phase. the output is the sine value from -1 to +1 for X and another -1 to +1 Y
Last edited by Architeuthis on Sat Jul 11, 2026 1:35 pm, edited 1 time in total.
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Music Engineer Music Engineer https://www.kvraudio.com/forum/memberlist.php?mode=viewprofile&u=15959 - KVRAF
- 4385 posts since 8 Mar, 2004 from Berlin, Germany
Mathematicians strongly suspect that pi is a so called "normal number"
https://en.wikipedia.org/wiki/Normal_number
which basically means that the probability distribution of (sequences of) digits should follow a uniform probability distribution. I think, this would mean that it should be statistically indistinguishable from the output of any old PRNG (up to the inevitable (hopefully long) periodicity of the PRNG, of course). So, I do not really see any reason to believe that "pi-noise" should be somehow special from a sonic perspective.
Nice to see that you now have your Chaosfly algorithm published. I think, it does interesting stuff and by exploring its parameter space, we may indeed synthesize interesting chaotic sounds. In your video, there are indeed little obvious aliasing artifacts - it's mostly noise, but: between 1:45...1:53 I hear something that sounds very much like aliasing.
https://en.wikipedia.org/wiki/Normal_number
which basically means that the probability distribution of (sequences of) digits should follow a uniform probability distribution. I think, this would mean that it should be statistically indistinguishable from the output of any old PRNG (up to the inevitable (hopefully long) periodicity of the PRNG, of course). So, I do not really see any reason to believe that "pi-noise" should be somehow special from a sonic perspective.
Nice to see that you now have your Chaosfly algorithm published. I think, it does interesting stuff and by exploring its parameter space, we may indeed synthesize interesting chaotic sounds. In your video, there are indeed little obvious aliasing artifacts - it's mostly noise, but: between 1:45...1:53 I hear something that sounds very much like aliasing.
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- KVRAF
- Topic Starter
- 3579 posts since 28 Jan, 2006 from Phoenix, AZ
what survives science, what gets thrown out:
WHAT SURVIVES (hard facts):
1. a pure sinewave below nyquist does not alias
2. a flat / constant value does not alias. no content above 0 hz, nothing to fold.
3. clipping generates harmonics, and any of those harmonics above nyquist fold back down. so clipping can cause aliasing.
4. a small number of feedback / modulating sinewaves can produce very rich spectra. fm synthesis already proves 2 oscillators make huge timbral complexity. my chaos generator is in that family.
5. aliased broadband noise still sounds like noise based on perception rather than reality, but perception is what we care about
WHAT I THROW OUT (does not survive science):
1. "pi takes more power per digit" - false. spigot algorithms compute digits directly (thanks BertKoor, Music Engineer).
2. "pis digits are special / the universes noise floor" - false. most real numbers are infinite and non-repeating, pi isnt special (Music Engineer). its just a convenient reproducible pseudo-random sequence.
3. "circles / sinewaves are self-similar / fractal" - false. zoom into a circle or a sine and it flattens toward a line, the opposite of fractal (jupiter8).
4. "0 == infinity", "-1 == +1", "x/0 = infinity" - false in standard math. x/0 is undefined, not infinity (jupiter8, Music Engineer).
5. "clipping == aliasing" and "breaking the laws of physics" - false. both are correct math, not law-breaking (stoopicus). related, per keep #3, but not equal.
6. "speed of light = 44100hz", "black holes = 0", "simulate your own universe" - not physics, not dsp. these were mnemonics to push my brain around. fun, but not facts, so out of the technical claim.
7. "mimic ANY sound with two sinewaves at infinite precision" - overclaim. the honest version is keep #4: a wide range, not literally anything.
WHAT ACTUALLY STANDS (needs none of the theory):
- superlove filter: recursive self-oscillating analog-style filter. feedback = mod*feedback + shaped(feedback), filtered before it feeds back. code linked earlier.
- chaosfly: 2D generator, a sine modulating a sine, both feeding back into freq and phase, filter in the loop, output x/y from -1 to +1. soundemote.io/sandbox.
OPEN EXPERIMENT: pi digits as a deterministic noise / dither source.
INTERESTING: a sine looks flat at extreme zoom levels. that same smoothness is why it's band-limited and doesn't alias. "looks flat when you zoom in" and "doesn't alias" are two views of the same thing: no sharp high-frequency detail.
("pure random") pi noise: https://www.youtube.com/watch?v=zdmK2_-3Mcg
("somewhere inbetween") chaosfly: https://www.youtube.com/watch?v=ah8ZGdGbFLM
("pure order") sinusoidal resonator: https://www.youtube.com/watch?v=m-_bo7PFUGI
("the use case") superlove filter demo: https://youtu.be/GmpdZk31ARc
WHAT SURVIVES (hard facts):
1. a pure sinewave below nyquist does not alias
2. a flat / constant value does not alias. no content above 0 hz, nothing to fold.
3. clipping generates harmonics, and any of those harmonics above nyquist fold back down. so clipping can cause aliasing.
4. a small number of feedback / modulating sinewaves can produce very rich spectra. fm synthesis already proves 2 oscillators make huge timbral complexity. my chaos generator is in that family.
5. aliased broadband noise still sounds like noise based on perception rather than reality, but perception is what we care about
WHAT I THROW OUT (does not survive science):
1. "pi takes more power per digit" - false. spigot algorithms compute digits directly (thanks BertKoor, Music Engineer).
2. "pis digits are special / the universes noise floor" - false. most real numbers are infinite and non-repeating, pi isnt special (Music Engineer). its just a convenient reproducible pseudo-random sequence.
3. "circles / sinewaves are self-similar / fractal" - false. zoom into a circle or a sine and it flattens toward a line, the opposite of fractal (jupiter8).
4. "0 == infinity", "-1 == +1", "x/0 = infinity" - false in standard math. x/0 is undefined, not infinity (jupiter8, Music Engineer).
5. "clipping == aliasing" and "breaking the laws of physics" - false. both are correct math, not law-breaking (stoopicus). related, per keep #3, but not equal.
6. "speed of light = 44100hz", "black holes = 0", "simulate your own universe" - not physics, not dsp. these were mnemonics to push my brain around. fun, but not facts, so out of the technical claim.
7. "mimic ANY sound with two sinewaves at infinite precision" - overclaim. the honest version is keep #4: a wide range, not literally anything.
WHAT ACTUALLY STANDS (needs none of the theory):
- superlove filter: recursive self-oscillating analog-style filter. feedback = mod*feedback + shaped(feedback), filtered before it feeds back. code linked earlier.
- chaosfly: 2D generator, a sine modulating a sine, both feeding back into freq and phase, filter in the loop, output x/y from -1 to +1. soundemote.io/sandbox.
OPEN EXPERIMENT: pi digits as a deterministic noise / dither source.
INTERESTING: a sine looks flat at extreme zoom levels. that same smoothness is why it's band-limited and doesn't alias. "looks flat when you zoom in" and "doesn't alias" are two views of the same thing: no sharp high-frequency detail.
("pure random") pi noise: https://www.youtube.com/watch?v=zdmK2_-3Mcg
("somewhere inbetween") chaosfly: https://www.youtube.com/watch?v=ah8ZGdGbFLM
("pure order") sinusoidal resonator: https://www.youtube.com/watch?v=m-_bo7PFUGI
("the use case") superlove filter demo: https://youtu.be/GmpdZk31ARc