Nova - Fractals: Hunting the Hidden Dimensions

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washparkhorn

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Amazing episode of Nova on fractals. Catch it on repeats if you can. If nothing else, the visual aspects are stunning.
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Excellent topic!

There is a free iPhone app that does Mandelbrot and Julia sets that I highly recommend. I haven't looked yet for anything similar to take advantage of big iron PC's with graphic cards.

Intrigued by a function that could plot so much irregular patterning on any scale, I discovered that this in not a cut and dry plug in an x and get a y value computation. From what very little I gathered, I vaguely understand at this point and likely incorrectly, that there is a lot of some kind of looping going on.

If I find a web site with a clear cut example I'll post.
 
I wrote a program that generates fractals in high school. The most popular visual fractals, like the Mandelbrot set, compute one point (or pixel) at a time. So your function inputs are x and y. Each point is a loop calculating the "escape time". The color at each point is the number of loops it takes to reach a certain point in the equation. Usually black is selected when you get close to an infinite loop. This gets pretty computationally expensive when you zoom in on the edges.

I bet this is a lot nicer on modern processors. The most popular software is totally free. It's called fracint.
 
Fractals have been important in subsurface earth modeling since the 70's. Tom Hewitt, who then worked for us but is now at Stanford, was one of the key figures of that time. The mining industry actually got into it earlier.

However, other geostatistical approaches have more or less displaced fractals as a modeling approach, at least as far as matching nature, in this particular domain.

Fractals are abstract mathmatical objects. Nature is nature: reality. The correspondence we see between the two is of a practical nature, created in our minds.
 
Isn't math our collective consciousness?

I viewed the programs as how we intuitively understand the patterns in nature, music, . . ..

Could be the pain meds though.
 
What I intended by my misstatement was that math is one thing, nature another, and we use the math pattern findings as practical tools in understanding nature. A current approximation.

Later posts bring up the idea of math as a separate reality independent of humans. I think the idea is called platonism, and it has notable adherents - Godel for one. To me, this seems like a matter of philosophical perspective, like the man-tree-woods issue.

If people couldn't percieve the patterns, would the patterns exist? Well, yes, but, pattern itself is a human construct.

While I would agree math is a "social" construct, i do not ahere to the post modern Kuhn view of science as a social construct is equivalent to any other idea, etc. That's a whole other thread.

Math is unique in that it is about abstract objects and their relations only, not about nature. We apply math to nature as a tool.

Happy Halloween.
 
Fascinating topic! I had heard of this subject, but did not know of any practical applications until now.
Will try to view the TV show-I saw it listed, but didn't know if it would be worth watching. Hopefully, it will air again.
 
watched it before frontline the other night. while it is way above my paygrade, it is fascinating stuff. who is going to tell all the religious nuts that God was seriously into math?
 
Fractals are awesome on many levels to include intellectually and recreationally. At some of the underground or renegade parties we would throw in DC and NYC we would project some on walls and ceilings much to the joy of party people in our place to be.

Geiss has some kind of screensaver that generates fractal type images and is pretty cool.

Ty for the heads up and yes, I will be looking for an episode to watch of it.
 
I like watching NOVA and similar shows, and feel I'm pretty smart and can understand the topic. I found I didn't fully understand what they were talking about during this show.

It may have been I was distracted with kids, and cooking gumbo for a party, but I doubt it. I just was lost on this topic...
 
Coel
I agree, there is much evidence to show that human appreciation of symmetry is a universal. This has many implications, sexual and mathmatical.

I still protest against this idea that fractal formulation is "natural" vs "unnatural" Euclidean form or any other "western" form (wasn't Mandelbrot western?). No abstract mathmatical object is "real" or "natural". This fractal form appears useful for some representations of natural processes. Again, it is manifestly not the "best" form, for natural processes in general. There isn't one.
 
Great thread - the philosophical debate over mathematics is a fascinating one. I recently read "Incompleteness", by Rebecca Goldstein, a slim and very readable account of Kurt Godel and his two incompleteness theorems. She gives a very detailed history of Platonism and it's place in various philosophical debates leading up to the Vienna Circle. I highly recommend to anyone here interested in the subject.
 
We're
To see Godel's "diagonal" proof in action, you should read Hofstader's account of it in Godel, Escher, Bach. Its almost like understanding it.
 
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