Tag Archives: mandelbrot

Fractalicious

25 Feb

So I’m really bad at math. I know a lot of people say that, but really, it would anger you how bad I am. I once tried to add 3 to 19, and somehow came out with 12. Really. Bad.

That having been said, there are some things in the mathematical world that I find simply fascinating. Like sacred geometry. YUM. I mean, I can understand visually how the golden spiral relates to the Fibonacci sequence,

but when I look at it expressed like this…

HA! What does that even mean?

But I love the visuals that math creates. I love seeing something beautiful come from a strict set of patterns and rules. And I’m mildly obsessed with fractals.

Benoit Mandelbrot, the French-American mathematician hailed as the father of fractal geometry defines fractals as “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole, a property called self-similarity.” Basically, a strict mathematical pattern that repeats itself into infinity by exponentially getting smaller. You’re probably more familiar with fractals than you think. Ever played Legend of Zelda? The triforce is just the beginnings of the Sierpinski Triangle.

Boom. Fractal.

No doubt the most famous fractal is the Mandelbrot set, named after the aforementioned father of fractal geometry, the late Benoit Mandelbrot.

The Mandelbrot Set is generated from the formula, z=z^2+c. I have no idea why.

Here’s a short video on the Mandelbrot Set that explains quite succinctly what appeals to me about fractals:

A form in which the boundaries of that form contain miniature copies of the entire set, and within that endless unique shapes. Strikingly similar yet mathematically unique shapes from the same formula repeating into infinity. There’s something just so elegant and somewhat tragic about that thought. I’ve decided that fractals are a beautiful way to wrap my senior thesis in the proper language. I’ll be posting more on my thesis as it develops, but for now, enjoy this TED talk from mathematician Ron Eglash on fractals that occur in African villages. If you don’t have time to watch the whole thing (which is fascinating), at least watch the first three minutes or so as they really delve into the beauty of fractals and how they occur over and over and over in the natural world.

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