Wednesday, September 2, 2009

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.



That was fun! I saw Pink Floyd in concert a few times; everything they play, 'evolves' much like this video (their music, I mean).

I think The Moody Blues and Pink Floyd were two musical groups who saw these shapes quite often during their experiences with LSD (well-publized in the news of course).

Like you, I always find something 'else' in anything I look at. I was a little girl when I fell in love with a kalidescope (I'm sure I've butchered that spelling, but it's close enough when my dictionary isn't......).

I actually keep a spare kalidescope in the car, for when I get bored 'riding' (which is why I do most of the driving). When it's dark, and there are no 'shapes to look at', I get out the scope and look into the oncoming headlights to see what kind of pretty shapes and different effects I can find.

A roaring fire at night also makes the most beautiful shapes; the leaping flames also recreate themselves, I think.

It was a fun and intriguing post, as well as video. Diane

ivan said...

would probably fail the Rorschach inkblot test , and I am surely more visceral than mathematical, but your first illustration makes me, for some reason, think of the old song by Freddiie Mercury, of Queen: Fat bottomed girls you make the rockin' world go round

kenju said...

I have seen fractals before, and I don't understand what I'm looking at - but I surely do enjoy it!!

PhilipH said...

Fascinating stuff. In the dim and distant past I used to have a couple of programs on an old pc and used to play around for hours just seeing how differing input variables made such patterns 'grow' on the screen.

Jo said...

Diane, I love kaleidoscopes. I think that's why I love fractals. And I have always loved staring into a fire as well..!

Ivan, you make me laugh right out loud. :-)

Kenju, I don't understand them either, but they are beautiful, aren't they?

Philip, there are fractal programs now, but I just never seem to have time to play with them. *sigh*

Brenda said...

My husband just walked by as I was reading this and knew exactly what I was looking at. He said he has some books about this. I go to Quilt Shows that have some patterns like these. Gorgeous!

Charles Gramlich said...

Lana and I just watched a special on this and she bought a book about fractals. Fascinating stuff from both a visual and a mathematical side.

eda said...