On 17 Sep 2012, at 22:25, meekerdb wrote:
But did anybody think z' = z^2 + c was interesting before that?
Yes. This was known by people like Fatou and Julia, in the early 1900.
Iterating analytical complex functions leads to the Mandelbrot fractal
sets, or similar.
The computer has made those objects famous, but the mathematicians
know them both from logic (counterexamples to theorem in analysis,
like finding a continuous function nowhere derivable), or from dynamic
system and iteration.
If you iterate the trigonometric cosec function on the Gauss plane C,
you can't miss the Mandelbrot set.
In nature too as the following video does not illustrate too much
seriously :)
http://www.youtube.com/watch?v=JGxbhdr3w2I
Bruno
Bretn
On 9/17/2012 1:17 PM, Terren Suydam wrote:
I would say computers were the tool that allowed us to see it, like a
microscope allowed us to see bacteria, and a telescope stars.
On Mon, Sep 17, 2012 at 3:14 PM, meekerdb<[email protected]>
wrote:
On 9/17/2012 10:36 AM, Terren Suydam wrote:
Rex,
Do you have a non-platonist explanation for the "discovery" of the
Mandelbrot set and the infinite complexity therein? How can you
make
sense of that in terms of the constructivist point of view
How can you make sense of it otherwise. The Mandelbrot set is only
interesting because it became possible to construct it by use of
computers.
Brent
that you
are (I think) compelled to take if you argue against arithmetical
platonism? It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated
on
z' = z^2 + c, but maybe I am missing the point of your argument.
Terren
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