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17 October 2010

Mandelbrot’s Fractals

Mandelbrot set rainbow colors

What is the Mandelbrot Set? "The Mandelbrot set is a mathematical set of points in the complex plane, the boundary of which forms a fractal." Read the complete definition on Wikipedia.  Or watch this 54 minute video:
(This is a television documentary from 1995.)

A very recent (Feb 2010) video from TED presents Mandelbrot talks about the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated :

"Benoit Mandelbrot: Fractals and the art of roughness"

There are two important words you need to know to understand what these people are talking about: fractal and pattern.

photo by Fábio Pinheiro 
fractal is "a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry" (link) like circles, triangles, etc.
pattern  is "a type of theme of recurring events or objects, sometimes referred to as elements of a set. These elements repeat in a predictable manner." (link)

We've certainly had experience with pattern in our learning at ISOCS, particularly in math and language. You've had experience with  fractals, obviously in screen savers,  the visualizer on iTunes or another media player, or with software ( link and link, or the Mandelbrot Explorer), and not so obviously in nature:  because most patterns in nature are fractals!

Fractal Tree by Solkoll 
Some of the phrases I heard in this video which caught my attention were:

"You don't need to know big math to understand this."

"Nature doesn't deal in smooth objects, but in fractals
the relationship between what we see as "nature" and the math rules behind it - what we are seeing is fractals, everywhere."

Cloud patterns are fractals

"The discovery of fractal geometry changes the kinds of patterns we can look for in nature."

photo by Dan4th 
"There will be extraordinary new devices based on the principals of fractal geometry that will emerge over the next centuries."

"Cauliflower is very complicated and very simple at the same time" (You can read the transcript of the TED video here.)

Read a little about Mandelbrot's life and work at Heroes and RoleModels.

Read more about the origins of the 1995 video at Open Culture, which  is, yet again, responsible for inspiring a post on this blog!