Mandelbrot Set and Fractals

1. Oct 1, 2011

Newtons Apple

Can someone explain the Mandelbrot set to me? I know the equation is zn+1 = zn2 + c
But what does this mean? Whats its basically saying here? All I know about it really is the existence of fractals, but why are fractals so mathematically important?

2. Oct 1, 2011

Bacle

It is a Mandelbrot set; one for each value of c. As the article:

http://en.wikipedia.org/wiki/Mandelbrot_set

the set contains the elements c for which the iteration you described, starting with zo=0 , is bounded under iteration.

Fractals are important for modeling and for dynamical systems.

Maybe this will also help:

http://math.stackexchange.com/quest...et-contain-slightly-deformed-copies-of-itself

You can search the site for more on fractals.

Part of the importance is that fractals model aspects of nature (clouds, jagged coastlines)
that are not easily modeled with standard geometric figures like staright lines.

Last edited: Oct 2, 2011