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Who says mathematics isn't fun? :-D
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...and now *with* the attachment I meant to add the first time...
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Attachments:
Download 'test_drawrk.jpg' (31 KB)
Preview of image 'test_drawrk.jpg'
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> ...and now *with* the attachment I meant to add the first time...
Go on then, what's the mathematics behind this one? Gravity?
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scott wrote:
>> ...and now *with* the attachment I meant to add the first time...
>
> Go on then, what's the mathematics behind this one? Gravity?
Well, I don't know about "gravity"... merely the damped oscilations of a
particle attracted to the center of the image.
If the force applied is proportional to the distance, you tend to can
spirals and sometimes stars. If the force is inversely proportional to
distance (e.g., inverse square), you get loops.
Now, if you add more than one attractor.....
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>> Go on then, what's the mathematics behind this one? Gravity?
>
> Well, I don't know about "gravity"... merely the damped oscilations of a
> particle attracted to the center of the image.
I should perhaps point out that the RED trace is the path of the
particle. The GREEN path is the object's velocity, and the BLUE path is
the object's acceleration.
...which means that there's no real way to correlate the three traces to
each other, which is kind of useless. Oh well!
> Now, if you add more than one attractor.....
...it goes completely scatty! o_O
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>> Now, if you add more than one attractor.....
>
> ...it goes completely scatty! o_O
It's called chaos :-)
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scott wrote:
>>> Now, if you add more than one attractor.....
>>
>> ...it goes completely scatty! o_O
>
> It's called chaos :-)
Well, if you wanted to be technical about it, it's "chaos" if
arbitrarily close starting points diverge violently. ;-)
But yes, I'm pretty sure this system possesses such a property. Now, to
graph it.....
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> But yes, I'm pretty sure this system possesses such a property.
It might depend on how much damping you give it.
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scott wrote:
>> But yes, I'm pretty sure this system possesses such a property.
>
> It might depend on how much damping you give it.
Doubt it.
Consider a point exactly between two attractors. A particle at this
point experiences zero resultant force. Purturbing the point by any
finite amount to either side will make the resultant force non-zero.
This will cause a different path to be traced, regardless of how much
damping is applied.
In general, applying more damping makes the system *less* unstable, but
does not remove areas of chaotic behavious; it just makes them smaller.
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Invisible wrote:
>> Now, if you add more than one attractor.....
>
> ...it goes completely scatty! o_O
Twisted and tangled, baby! :-D
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Attachments:
Download 'test_drawmany.jpg' (48 KB)
Preview of image 'test_drawmany.jpg'
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