The Mandelbrot Set

The Mandelbrot set, named after Benoit Mandelbrot, is a fractal. Fractals are objects that display similarity to the original shape at various scales. In other words, if you magnify a fractal, it seems to be duplicating itself. The process of generating a fractal is based on an extremely simple equation involving complex numbers. That’s about as much as I understand about the Mandelbrot set. Most of you probably understand more about fractals and the Mandelbrot Set than I do. No one could ever mistake me for a mathematician. I am fascinated, though, with the shapes that fractals produce, and the thing that amazes me is how the Mandelbrot set resembles a human figure.

I have always loved finding shapes in other shapes. I never just look at a tree or a flower, or a chair. I find other shapes within the shapes of those objects. Art and mathematics are two sides of the same coin, and mathematics is at the heart of all beauty. The eye likes symmetry, even in chaos, and a mathematically correct picture will be more pleasing to the eye than one that is not. Jackson Pollock, Picasso, Rembrandt -- all different styles -- but all mathematically correct. And Mozart’s music is said to be mathematically perfect, and therefore beautiful to the ear.

Looking at this strange little video always gives me goose bumps. It’s like looking into the eye of God at the moment of creation. As you can see in this video, these exquisite, intricate shapes are made by mathematical equations. After first seeing this a few years ago, I was never able to look at shapes the same way again. The next time you are out for a stroll in the forest, take a look at the shapes of the ferns growing along the path, and you will see fractals. Or gaze closely at a perfect daisy, and you will see the mathematical equations that created it.