"Bill Pragnell" <bil### [at] hotmailcom> wrote:
> "Robert McGregor" <rob### [at] mcgregorfineartcom> wrote:
> > "Bill Pragnell" <bil### [at] hotmailcom> wrote:
> > > I might try an animation using my sphere technique,
> > > if I turn off AA they only take a minute or so.
> >
> > This morning I found this morph animation in a subfolder of my attractors
> > folder; I had completely forgotten about it! Originally rendered as an 1920x1080
> > (HD) AVI, I just squashed it down into this little MPEG-4 to post here.
>
> That's fascinating! I take it these two attractors use the same set of
> equations? It looks like it - there appears to be a certain congruence between
> some of the features (if that's the right phrase!).
>
> I've got to try this!
>
> :)

Well, my little app calculates Lyapunov exponents based on some random numbers,
looping over the function until I get lucky and the series doesn't tend toward
zero or infinity. Then it creates 100,000 or so particles and draws a preview in
the viewport. If I like what I see I can click a button that saves the data as a
POV include file (an array of vectors) along with the preview bitmap, or click a
"Try Another" button to start over. I saved off more than a hundred interesting
varieties over the couple of weeks that I was exploring these types of
attractors.

Something I found really exciting and fascinating was seeing a real-life
attractor a couple of months later, one I thought I recognized from my
experiments! It was early June, 2007, nearing sunset here on the east coast of
Florida and the space shuttle had launched about 15 miles from my home. Some
weird chaotic upper air currents were doing an attractor dance up there and the
smoke trail left by the shuttle showed the pattern. I grabbed my camera and took
a few shots for posterity. Here's the attractor saved by my app preview and the
similar real-life version:

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