>The Mandelbrot set, charming as it is, is in no *special* position to
>shed light on this issue. It is simply one of zillions of complicated
>mathematical objects that mathematicians study,
To the contrary, the mandelbrot set *is* a "special" mathematical object.
It is similiar to PI in its specialness.
It can be found involved in the behaviour of many fractal objects which
initially may seem to bear no relation to the mset.
For example, there is a famous fractal one obtains by simulating this:
Put down 3 magnets in an equilateral triangle, and suspend an attracted magnet
above them by a pendulum. Color the magnets red green and blue. Put the
pendulum at some initial point, let it go, and whichever magnet it finally
comes to rest at determines how you color the initial point. As you do this
(on a computer) to increasing resolution you get a very pretty fractal.
NOW - begin varying parameters of the problem, such as the magnetic strength,
distances involved, force of gravity etc.. I unfortunately forget which ones
in particular. But now create a New fractal which is an evaluation of the
effect of these parameters. (For example gravity on the X axis, Magnetic
strength on Y) and Lo and behold! You get a new fractal which upon exploration
is found to contain the mandelbrot set.
Sorry this is rather a long post, but i find it very intriguing. I don't have
the reference for this onhand, but if pressed i can try to find it. Cheers!
--
[infinity loves you, baby]
