(working title) 2 dimensional chaos generator

[antto]

well, since i can not make sense of this, i think there are generally two possible options
A) you are going in circles
B) you are actually going to invent something that is unthinkable to most other people, which would explain why those very people are unable to understand you right now, but it also means they cannot help you. so you're probably gonna have to walk to there alone (or waste time here trying to convince the blind that there is light and it has colors and stuff)

[Architeuthis]

hint: you can use numbers outside -1 to +1 but they should be considered runaway values (a stable value of 2.0 is a runaway value that doesn't move. another infinity of 0 change)

[Architeuthis]

2.0 repeated 44100 times a second, you have self-similarity through time, therefore flat signals do not alias. self-similarity / fractal / infinitely detailed.

[Architeuthis]

logic jump: if it is not infinitely self similar through time it must be infinitely self similar through space. a thing must exist somewhere between those two truths to not break the laws of physics... or something? this is the limit of what i can ponder

[antto]

careful: i knew a guy who mixed DSP with Religion (in fact, he was on this very forum too, among other places... guess why i said "was")

[Music Engineer]

We all operate on assumptions based on experience and evidence. If you go down to the fundamentals of math then it is all just based on logical rules (which, I think, are pretty much undisputable) together with axioms (some of which (if we talk about ZFC) may be disputable - many take issue with the axiom of choice (the C in ZFC), I personally find the axiom of infinity harder to swallow). Russel and Whitehead (in)famously took 300+ pages of dense math to prove that 1+1 = 2. The proof appears on page 300-something in their book.

https://en.wikipedia.org/wiki/Principia_Mathematica

The point is: Yes, you have to, at some point, accept certain things as true without proof. These are the axioms. Axioms should be as obviously true as possible. And then there are also the logical inference rules that you have to agree upon. But as said - I think, they should be fairly uncontroversial.

[Architeuthis]

The point is: Yes, you have to, at some point, accept certain things as true without proof.

there is one undefined that you are allowed. a single value. a singularity: pi

[Architeuthis]

the neverending decimal values of pi is the noise floor / background radiation of the universe... my universe. (not actually, i havent done the math).

hypothesis: the noise floor may not break the speed limit / laws of physics, and does not.

[Architeuthis]

noise is finite(-coded? to be random you need time) (random, one number after the other), sine is infinite (self-similar)
noise is not self-similar through time and not self similar through space.

[Architeuthis]

to be random you need time to prove that you are random. but it takes infinite energy to prove something is infinitely random because you need to check for the entire simulation.

[Architeuthis]

wouldn't you also need to check for fractals within the infinitely long random number? so now you're stuck within being stuck trying to prove if it was perfectly random.

you could average it, but you would need to average the entire universe.

[Music Engineer]

The neverending (and never repeating) digits of pi are actually not so special. Most real numbers are like that. The rational numbers (i.e. those with a finite or periodic decimal representation) are in a mathematically precise sense infinitely sparse within the real numbers. This is true even for all numbers with an algorithmically representable decimal representation (computable numbers). This is the distinction between countable infinity and the continuum.

[Architeuthis]

so yes, spigot formula breaks my logic.

[Music Engineer]

I don't understand them either. I just know that they exist and find that remarkable.

[Architeuthis]

im working on the spigot noise generator to see what the noise profile is like. in the meantime, this is running at 44100, the filter is a simple algorithm:

Code: Select all

feedback = mod * feedback + input        // the loop's memory
osc      = sin(feedback * 2π)            // sine, phase-driven by its own past output
feedback = onePole(osc, cutoff)          // filter it before it feeds back
output   = feedback

the code represents a recursive formula for creating an analog-style filter with many settings depending on how you control cutoff, feedback, shaper

FULL CODE: https://github.com/soundemote/soemdsp-s ... filter.cpp

edit: the ai made the code too verbose. it will be condensed at some point

for easier to read code find superlove filter here:
https://gitlab.com/Hickler/soundemotefr ... lterCore.h

here it is spelled out as condensed as possible (missing curves for variables):

Code: Select all

double getSample(double in) override
{
	// input and feedback signal
	feedbackSignal = mod * feedbackSignal + inputAmplitude * in;
       
	// self oscillation
	double oscValue = -waveshape::trisaw(feedbackSignal + 0.25725, shape);

	// feedback filter
	feedbackSignal = filter.getSample(oscValue);

	// final out
	return dcfilter.getSample(feedbackSignal) * 1.02;
}