That's awesome. I wish I could have thought of that. I wonder what kinds of applications this could be used in.
I just have one question. Suppose you replace all parabolas by straight lines. That is, no sqrt; the first parabola becomes a line with slope 1 (y=x), and the other parabolas would be replaced by lines with slopes 2,3,4,... (the lines y=2x, y=3x, y=4x, ...). As you draw horizontal lines passing through the marks on your first line (the one with slope 1), would that horizontal still intersect none of the marks on other lines only at prime numbers of the first line?
Well, there is a sqrt(). Do an experiment: change all your sqrt() to log() in your Flash code, just like that, and then tell me if anything significant has changed. Even better: change all the calls to sqrt() to some function defined by you, thefun(); there you can play with returning sqrt(), log(), or whatever.
I've been skimming through your code, and I'm wondering where are you introducing the tan(acos(z)) part, because I can't find it.
srfriggen: you may want to start a new thread with your question. Personally I don't have an answer, but someone else may.
To be clear, I'm talking about the orthogonal projection onto the time axis as regards sin with the "directly mark" part here: "intersection of these divisions on the unit circle directly mark the deformation points of the fundamental frequency’s sinusoid"The intersection of these divisions on the unit circle directly mark the deformation points of the fundamental frequency’s sinusoid when you “mix” the two frequencies (fundamental + harmonic), hence the my comment on the link to the Fourier series and harmonic analysis.
Oh yes, I definitely understand that and I know my animation does not show the mixing of the sinusoids, it just shows one at a time. What I intend to show is how FFT can be used to identify prime harmonics. A prime number harmonic will only have energy at its frequency and its fundamental (1) across the spectrum, whereas a composite number harmonic will have energy at all its factors across the spectrum. ex: a 1/4 or 4th harmonic of a fundamental frequency will have energy in the 1/2 or 2nd harmonic. Make any sense?Hi, Jeremy,
surely you realize that, in those sites that you cite, sinusoids are being added together. A formula that looks something like this is used,
f(x) = a1 sin(x) + a2 sin(2x) + a3 sin(3x) + ...
where the a1,a2,a3 are the amplitudes (the ones controlled by different slides on those pages).
This is what I fail to see in your drawing, where the sinusoid just stands alone in the middle of the unit circle, and that is why I made the remark about it being used only to split a segment in equal parts.