"WE'RE NOT IN KANSAS ANYMORE"

"A New Look at the New Math - The REALLY New Math"

Michael Round

July 20, 2009

New-Book-Announcement - and a Few Pages

THE MANDELBROT SET

THE SIMPLEST EQUATION IN THE WORLD

What comes to mind when I say the word “geometry”?  Triangles?  Spheres?  Generally, shapes – and maybe proofs regarding the similarity of triangles, distance formulas, and the Pythagorean Theorem? 

What shape is a basketball?  A sphere.  What shape is a football field or basketball count?  A rectangle.  How do planets orbit the sun?  Elliptically.  The answers come so quickly I’m certain I know quite a lot about geometry. 

What about a fern?  The clouds?  A snowflake?  Do these even have “shapes”?

These are all the result of nature, and they’re not “math-related”, you may be thinking?  I thought the same thing, once.  I now realize my idea of “math” is a poor one.  It’s particularly poor when I see the following created by a very simple math formula / process:

What is this?  What is going on here?   All of the images are the result of zooming in on the upper-left image, and all are created by the same math formula / process.

Here is the upper-left image, enlarged.  This is the Mandelbrot Set.

This isn’t the math you’re use to seeing?  You’re right.  It’s a brave new world!

It’s a world with an amazing story about an amazing man who developed the word “fractals” and discovered the above graphic using a very simple mathematical process.  Until the discovery of the computer, however, such a process was theoretical only; the shear amount of computations required to create this was insurmountable.  However, in 1979, Benoit Mandelbrot undertook this problem with the aid of computers.  What exactly did he do?  More importantly, can I do it?