Benoît Mandelbrot, Dies at 85

[jamesr]

I just saw the news that Benoît Mandelbrot died a few days ago (14th Oct)
http://www.nytimes.com/2010/10/17/us/17mandelbrot.html

I think it is fair to say that it was my first introduction to fractals, and writing my first program in BASIC on my ZX Spectrum in around 1985 (age 12), that opened my eyes to the beauty of complexity in the natural world.

It was then that I suddenly appreciated that the deterministic nature of physics as described by maths means even if a system seems random, or too complicated to understand. It is still driven by the same simple rules. From that day I new my path would be in physics.

So if something as complex as the Mandelbrot set can be described by the simple mapping of z->z^2+c, then the rest of the Universe may not be beyond our grasp.
That was 25 years ago…

Now, I find myself working on trying to describe the nature of turbulence in plasmas, where the self-similar (ie. fractal) appearance of eddys over a range of scales can tell you about how energy is distributed and dissipated.

[Brian H]

Indeed!

Big fleas have little fleas
Upon their backs to bite ’em.
And little fleas have lesser fleas,
And so ad infinitum!

So, how soon can we expect your one-line fractal TOE equation to be ready? :cheese:
And how many iterations before it gets down to the level of strings, and what then? :-/

[Ivy Matt]

Requiescat in pace.

[Brian H]

Evolution is also fractal?

Third, the history of life is fractal. Take away the labelling from any portion of the tree of life and we cannot tell at which scale we are looking (see diagram). This self-similarity also indicates that evolutionary change is a process of continual splitting of the branches of the tree.

Fourth, we cannot rewind, as Stephen Jay Gould argued in Wonderful Life. Were we to turn the evolutionary clock back to any point in the past, and let it run again, the outcome would be different. As in weather systems, the initial conditions can never be specified to sufficient precision to prevent divergence of subsequent trajectories.

[Rezwan]

Brian H wrote: Evolution is also fractal?

Cool, but I don’t see the puzzle here.

Puzzled by types of mollusc that abruptly disappeared from the British fossil record, apparently in response to a glaciation, only to reappear 2 million years later completely unchanged, he asked of Darwin: “Be so good as to explain all this in your next letter.” Darwin never did.

Um…perhaps the molluscs went on vacation to France, and returned (well, their great great ^n…grand molluscs) when the weather improved? Or when anti-immigrant sentiment got unbearable in France.

[Author]

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