Benoit Mandelbrot, your your fractal geometry was brilliant and your work revealed so much about the order and structure of the natural world around us.








On other news, along the same vein as Kinsey or Pollock, a movie about the life and work of Dr. Mandelbrot will be made and released in 2011. It's reported that producers are seeking out this exceptional actor to play the role...








[Edited on October 16, 2010 at 9:26 PM. Reason : ]

10/16/2010 9:25:51 PM

He would often make wild and bold conjectures about mathematics and leave lesser minds to actually prove them

naturally the mathematical world was not amused

10/16/2010 9:31:18 PM

Dude was ridiculed by his colleagues for researching fractal geometry at first. They were all like "This shit is dumb and you are dumb." He later was like "Booya, I am smart and fuck you"

10/16/2010 9:32:58 PM

Quote :

"YOUR YOUR FRACTAL"

4/2/2024 12:19:46 AM

GNSP

4/2/2024 12:29:03 AM

gn...sp

4/2/2024 2:11:31 AM

someone is going to have to explain this to me like 7th grade style

I've been reading about it but I don't understand what it means about people able to infinitely zoom in

so what does it mean in the black parts of it? it seems like the black one would just stop

ok that may not be coherent enough to follow sorry

4/2/2024 2:14:45 AM

I've watched a couple of videos and am at like 20% knowing what's going on

4/2/2024 2:58:07 AM

oh what could've been

4/2/2024 4:21:51 AM

SL,SP

4/2/2024 8:01:12 AM

^LOL! He used to work out with Charles Atlas in the '50s!

4/2/2024 8:30:33 AM

^^^^^

I'm not sure if this is what you're looking for, but the Mandelbrot set is in the complex plane. The complex plain is made up of complex numbers, which are numbers of the form a+bi, where a and b are any two real numbers and i is the imaginary number where i^2= -1. You get a plane out of them by putting them on the xy-plane: For example, 5 - 3i corresponds to the point (5,-3) in the xy plane.

So to get the Mandelbrot set, you start with some complex number c (= a +bi for some real numbers a and b). Take that number, square it and add c to the result. Now square that, and add that original c to the result. Keep repeating this over and over again. If the results stay around the origin (0 + 0i, or just (0,0)) in the xy plane, no matter how many times you repeat, then that c is part of the Mandelbrot set (which makes up the black area in your video). Otherwise, those results will get farther and farther from the origin without bound, and those points are not in the Mandelbrot set (I put a couple of examples below). These are the colored points in the video; the different colors represent how quickly the results speed away from the origin. And the Mandelbrot set has a fractal boundary, which means when you zoom in on it (meaning like a microscope would do) you see infinite complexity (and self similarity) no matter how far you zoom in.

A couple of example of the calculation above:

If start with i:

Square it, then add i and you get -1 + i

Now square that, add the original i again:

(-1 + i)^2 + i = (1 - i - i -1) + i = -i

(the part in the parentheses came from just distributing (or FOIL, which a mnemonic often used for it) (-1+i)*(-1+i).

Now do it again: Square the result and add the original i back: (-i)^2 + i = -1 + i, which is the same number we had from a couple of steps back, so that means from here it will just repeat forever:

-1 + i

-i

-1 + i

-i

-1 +i...........

These numbers do not get further and further from the origin, so i is part of the black Mandelbrot set.

On the other hand, if you start with 1:

1^2 + 1 = 2

2^2 + 1 = 5

5^2 + 1 =26

26^2 + 1 = 677....

And from here it should be obvious it'll just keep on getting larger and larger without bound. So 1 is not in the Mandelbrot set; it would be one of the colored points.

Does that make sense?

4/2/2024 5:28:04 PM