if not strangely so....

J. C. Sprott, some years back, alphabetized the parameters of the 
general quadratic map,

X_n+1 = C0 + C1*X_n + C2*X_n*X_n + C3*X_n*Y_n + C4*Y_n + C5*Y_n*Y_n

Y_n+1 = C6 + C7*X_n + C8*X_n*X_n + C9*X_n*Y_n + C10*Y_n + C11*Y_n*Y_n

(X_0, Y_0) = (0, 0)

(see:

http://mathworld.wolfram.com/StrangeAttractor.html ),

by starting with A = -1.2, B = -1.1, ... Y = 1.2  (I toss in Z = 1.3, 
why not?)

So, MATTHEWSDAVE produces an apparently 1-dimensional (so not strange)
attractor.

I know others have made much nicer images of quadratic maps using 
POV-Ray, but since I made up a scene file that lets you input strings 
and see the attractor (if it exists), as well as one that randomly 
searches for attractors, using "clock," then spits out pictures you can 
sort through later, and I'm posting them to PBSF, I thought I'd share a 
couple of images, including my attractive name ;-)

One of them was produced with the random generator (note fewer dots so 
it parses faster), and the other is the same attractor done up nicer 
using the alphabet scene file.

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Attachments:
Download 'name.jpg' (37 KB) Download 'qm_random14.jpg' (49 KB) Download 'qma3.jpg' (73 KB)

Preview of image 'name.jpg'

Preview of image 'qm_random14.jpg'

Preview of image 'qma3.jpg'

Dave Matthews wrote:
> if not strangely so....
snip
> 
> So, MATTHEWSDAVE produces an apparently 1-dimensional (so not strange)
> attractor.
> 

On zoom, it is fairly clear that the attractor has a fractal dimension. 
  So, my name is strangely attractive (as well as having been usurped by 
a singer/band.)

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Download 'namecloseup.jpg' (57 KB)

Preview of image 'namecloseup.jpg'

Hi,
Nice! Could you post the script ? ;)
Thanks.

Dave Matthews wrote:

> if not strangely so....
> 
> J. C. Sprott, some years back, alphabetized the parameters of the
> general quadratic map,
> 
> X_n+1 = C0 + C1*X_n + C2*X_n*X_n + C3*X_n*Y_n + C4*Y_n + C5*Y_n*Y_n
> 
> Y_n+1 = C6 + C7*X_n + C8*X_n*X_n + C9*X_n*Y_n + C10*Y_n + C11*Y_n*Y_n
> 
> (X_0, Y_0) = (0, 0)
> 
> (see:
> 
> http://mathworld.wolfram.com/StrangeAttractor.html ),
> 
> by starting with A = -1.2, B = -1.1, ... Y = 1.2  (I toss in Z = 1.3,
> why not?)
> 
> So, MATTHEWSDAVE produces an apparently 1-dimensional (so not strange)
> attractor.
> 
> I know others have made much nicer images of quadratic maps using
> POV-Ray, but since I made up a scene file that lets you input strings
> and see the attractor (if it exists), as well as one that randomly
> searches for attractors, using "clock," then spits out pictures you can
> sort through later, and I'm posting them to PBSF, I thought I'd share a
> couple of images, including my attractive name ;-)
> 
> One of them was produced with the random generator (note fewer dots so
> it parses faster), and the other is the same attractor done up nicer
> using the alphabet scene file.

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stingo <sti### [at] listru> wrote:
> Hi,
> Nice! Could you post the script ? ;)
> Thanks.
>

Thank you!  It's already posted in povray.binaries.scene-files.

Dave Matthews

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