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4 out of 5 people found the following comment useful :-
lots of colors, and David Gilmour, 1 August 2006
Author: MisterWhiplash from United States

This is the kind of film that you'll likely find, and possibly watch if it's in the right 'mood', amid your friend's lot of obscure DVD's. Apparently that's how I came across it, as my friend was a big Pink Floyd- and more so David Gilmour- fan. As I understood what went on screen, Arthur C. Clarke talks to the audience about special things out in the universe. Particularly what are called 'fractals'. What was really most interesting about it all was the idea that such fractals, which continue on and on into infinity, it may connect to what happens with human revolution, or really how it connects to how the universe works. How, perhaps, things keep going in spirals. You don't have to be an astronomer to get what Clarke is talking about, but it does take some paying attention to. There are many little points made that, regrettably, flew over my head until I heard the intriguing key point about fractals. On the other hand, if you might happen to be looking for a little obscure stoner quickie, look no further. There's lots of staggering guitar solos by Floyd guitar maestro Gilmour that matches up well with the visuals provided. Make no mistake, the term 'trippy' does apply to these fractals, and it's probably a must-see in some circles. Though I probably wouldn't go out of my way to reach out for it.

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7 out of 11 people found the following comment useful :-
Mind bending, 2 March 2006
10/10
Author: ablebravo from gulf coast florida

This is a fantastic yet completely understandable documentary which discusses in detail the phenomenon of Fractal geometry. Sir Arthur Clarke does an excellent job of never talking down to his audience, yet imparts a great deal of detail in an enjoyable fashion. Interviews with other mathematicians including Prof. Mandelbrot himself adds to the intellectual appeal of this great (and not nearly long enough, IMO) production. The Fractal graphics are utterly breathtaking, and are aided by a perfectly composed musical score by none other than Roger Waters of Pink Floyd fame. The Fractal animations alone stand up to repeated viewings for no other reason than they are spectacularly beautiful. Totally recommended! Ten stars out of ten!

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4 out of 6 people found the following comment useful :-
Nice, but flawed, 29 December 2006
5/10
Author: schaduwtje from Netherlands

*** This comment may contain spoilers ***

It was great to see a documentary on math, as there aren't too many. This one even contains the great science fiction writer Arthur C. Clarke , the famous scientist Stephen Hawking and the inventor of the subject, mr. Mandelbrot himself. Not much that can go wrong one would think. Unfortunately it can go wrong, as is proved by this documentary.

The subject was basically about fractals, and more specifically the Mandelbrot set. Now, I am a computer scientist so I am familiar with the field. I understand that you cannot present complex formulas, because those are not comprehensible by the general public. Well, the big advantage of the Mandelbrot set is its simple formula, so that was not too big of a problem here. However, the way it was presented I liked less. They basically say, truly genius problems can be described in a very simple way. Newtons gravity laws are simple and Einsteins E=mc2 formula is simple and they where brilliant. Mandelbrot set's formula is equally simple, so it must also be brilliant. I don't like that kind of reasoning. Furthermore they show the formula, but do not really explain how it works. They only give hints that you can substitute coordinates in a plain in the formula.

What follows is a bunch of fractal animation. Yes, of course, plots of fractals look beautiful and are fascinating because they go on into infinite depth. However, showing the fractals over and over and over again, for like 25 minutes in a 50 minute documentary, even though accompanied by Pink Floyd music, was just too much. It didn't add anything to the documentary. It just "looked cool".

Furthermore, drawings of fractals resemble nature to some degree. That point was made and is correct. However, the documentary keeps going on about this, and also makes comparison that I find quite weak. For example, in the universe you can get from very large scales to microscopic very small scales. In fractals you can also from large scale to "deeper" scales. It is then suggested that this is the same thing. Give me a break. This property holds for every infinite recursive function and this aspect in my viewpoint doesn't add any 'validity' to fractals.

Also the appearance of Stephen Hawking, the most well known scientist in the world alive, was really a missed opportunity. The question was if the universe is also without boundary and goes on into infinite smallness like fractals. Hawking explains in two sentences that this is not the case, the smallness of the universe is confined to the Planck-length. "Aha", says Clark, "so this is not entirely like the infinite Mandelbrot set. Well, maybe the scientists are wrong, they don't know for sure either.". So Hawking only weakens the similarity of fractals with nature and then is easily dismissed. Is that a missed opportunity or what?

The very last part of the documentary is kind of OK again. It is explained that fractals are still 'new', and that we don't know what we can do with it yet. Then they speculate on some possible fields of application. However, what I didn't like was that it was a lot of "fractal-commercial-time". They told it in the manner of "fractals are magnificent, the possibilities endless, and it will change science and the world forever like Newton, Einstein, computers did". Uhu. Sounds a bit presumptuous for a unproven technique that is able to describe certain geometric objects. Don't get me wrong, I have nothing against the techniques themselves, they are great and potentially wonderful, I only have problems with the way it is presented here.

Oh, and the the religion-connection really came out of nowhere, and was plain terrible. I won't even discuss that. Luckily it was only briefly mentioned for a minute or so. Even uglier was when Michael Barnsley, the inventor (and patent-holder) of fractal compression, explains that the technique came to him by a dream, and that he finally understood the dream when his father died, or something like that. This is just thrown in for sentimental value and you can see on his face he doesn't even believe it himself. Yuck!

So what should be different in this documentary to my opinion? Well, it is never explained what techniques already existed and how fractals "fill the gap". It is never explained how Mandelbrot came to his famous equation, or how other mathematicians reacted on it. Furthermore, I really also would have loved to hear about the limitations of fractals. For instance, at one point fractal compression for digital pictures is discussed, however only the positives side to it. No one also explains that

- fractal compression only outperforms jpeg on very low resolutions

- fractal compression requires massive computation, magnitudes more compared to other techniques

- there are huge technical problems with fractal compression, i.e. automatically generating an optimal fractal representation of an image is still extremely hard and requires human intervention.

In the documentary the compression is presented as already "a real life application" (the documentary dates from 1995), while the given example is just composed. This really felt like a fraud and had just "give us more funding" written all over it.

So, to wrap things up. A documentary on math, or fractals in particular, is great. But next time, please go into depth, if not the math itself, then on the pros and cons of the techniques used and maybe the context in which the technique is invented. Don't give a presentation of 'nice images' that go on forever, with some rock music to make the field 'cool', just stay true to the subject.

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1 out of 1 people found the following comment useful :-
This is the very best explanation of fractals ever presented, 20 March 2008
10/10
Author: umpire63 from United States

"Colors of Infinity" is the very best explanation of fractals in general and the Mandelbrot set in particular ever presented. Arthur C. Clarke's soft-spoken style sets the "common man" at ease, and his pinpoint commentary makes the concept of fractals easy to understand. One need not be a stellar mathematician to grasp the concepts and why they are profound. The experts are trotted out, and they, too, explain fractal geometry in ways that are accessible to everyman.

Fractals are part of our lives, and math informs everything that exists, whether natural or man-made. When I saw this on TV several years ago, it reminded me of the Douglas Adams (of "Hitchhiker's Guide" fame) book "Dirk Gently's Holistic Detective Agency." In the novel, a software engineer tries to create a program that sets the flapping of a bird's wings to music using mathematical equations. That is exactly what fractals seem to do; they describe events in nature in mathematical ways, and the section of "Colors" which discusses this is eye-opening.

Whether you think you would be interested or not, give this show a viewing. You will be glad you did.

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