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  1. #1 Random from non-random 
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    This is all completely hypothetical and has no basis in the real world except by analogy. Assume you had an infinite energy field (and that this has no other implications other than it is just an infinite energy field), and we can describe this field as a number line from 0 to infinity. Along this line we have an infinite number of waves interacting, each with a different frequency, constituting every possible number from 0 to infinity. Now we start the time at 0 and let all the waves play out, and what do we get? All the waves with non-prime frequencies would be interfered with, and all the primes would not. As the order of prime numbers has no percievable pattern, results would not necessarily be predictable. Just a little something to think about.


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  3. #2  
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    I think we'll need a mathematical description of this to give an answer.

    I think you are asking about:

    You could also be talking about: , though I guess those are fairly similar.

    Or were you asking about something 3-dimensional? Or did I misunderstand something entirely?


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    Um, I'm kind of an amateur, and those formulas are for the most part meaningless to me, I'm sure you probably know what I'm talking about better than I do. If you could explain the first formula to me I would be most appreciative (don't waste your time with the second one since I won't know integrals til next semester). And as for 3-dimensional, I'd prefer that my head didn't explode, at least not today.
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  5. #4  
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    Well, then you probably meant the first one then.

    Basically it says take the sum of for all . Having said that, I really don't know much about the properties of this equation. Without actually checking, I'd pretty sure that it's aperiodic, but that it would occasionally become unbounded, especially near x=0, t=0.
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    Lol, I'm still not sure if that's what I'm thinking of or not, but thanks for explaining. I found a simple way to approximate what I'm talking about on a graph. Basically I just take a simple sine wave with a period of 2, so that at 0, it's going straight and at 1 its going straight down. I then have straight up be equivalent to 1 and straight down be equivalent to -1. If the sine-wave is any sort of sideways at x, I make it 0. So I overlap sinewaves with periods of 2, 4, 6, 8, and 10 and take the sums of the up/downess as a calculation of interference and I discover an interesting phenomena that relates back to the phenomena of the octave in music. There is a place in each graph 2,4; 2,4,6; 2,4,6,8; 2,4,6,8...x; where the graph of 2,4...x/2 fits in EXACTLY (when computing with integer values).

    The graph of 2 and 4 overlapping is the last symmetrical one. All after that are asymmetrical with greatly varying asymmetricality.
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  7. #6  
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    Use cos if you want it to be flat at 0. ()

    In music, an octave corresponds to a doubling of the frequency. The standard A is 440 hertz. So if t is measured in seconds, then , fed through a speaker, will produce an A. Then will also produce an A, just one octave higher. (Sin would do the same thing, just with a different phase. I'm not sure if humans can hear phase.) I guess you might have already know this, but oh well.
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    Thank you MagiMaster, I'm slowly being able to grasp these equations a little better. I'm rather new to calculus (obviously) but I wish to see if a few of my predictions are true, namely, that definite spikes will become apparent though fuzzy in overlaps of 2 through a relatively small x, and will become more defined as x tends toward infinity. I'm capable of doing this manually but the number of spikes jumps from 25-30 (can't remember exactly) at 4 overlaps to 249 at 5 overlaps (i.e. the number of spikes before the whole pattern repeats itself). Do you or anybody know of any computer applications I could use to help model this problem? If so, it would be greatly appreciated.
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  9. #8  
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    By spikes do you just mean peaks or do you mean peaks greater than a certain height?

    Also, if you're just using sin(i*x) or cos(i*x) then the period will just be , so that might help (or you might have already worked that out ).

    As far as software goes, either MatLab or Mathematica is good, but expensive. I don't know of any good, free software unfortunately.
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