|Fantasy cover using a fractal dragon|
Mandelbrot did something that crossed the boundaries between art and science, bringing art to science and science to art. He discovered and explored the principle of fractals.
Mandelbrot is said to have began working on his concept when he studied the Coastline of England, which, the more closely you measure it, the more it grows in length. Now, that, I understand. How can a coastline be measured, anyway? At what time of day do you go to make your measurements? High tide? Low Tide? And how high would high tide have to be? The more detailed you make your measurements, in and out of crevices and crannies, the longer the distance will become. Even if you only measured a portion for one hour, that distance would have changed during that hour.And you can't go back the next day at the same time to continue your work because the tides change every day.
True fractals are built of tinier fractals, so that if you magnify them, you can see even the lines are made up of the same repeated form. Magnify even 2,000 times, and you'll see them, theoretically in infinite magnification.
I don't begin to claim any more than a basic understanding of his concepts. I'm like most people who have a preliminary grasp of repeatable patterns in nature and art. That's all. But I have admired the concept, and seen it flourish in popular imagination and art. I've used the (royalty free) designs of others in my own designs because I find the symmetry fascinating. It's like snowflakes, or fern leaves. It's a new kind of geometry that can be used to analyze or portray complex shapes that were previously thought to be unmeasurable, or too complex to be described by Euclidian, or what most of us know as high school Geometry. As near as I can figure, that means finding regularity in shapes that appear to be random.
|A butterfly designed from fractal|
segments, artist unknown
|fractal spiral design, artist unknown|
That's too much for me. It's all an interesting conundrum, but I'd just as soon leave it as unexplainable, unmeasurable, for I'm not a mathematician. What I find fascinating is the effect this idea has had on computer-generated art. Fractal-building software can now take a complex shape and repeat it, repeatedly, in varying sizes, to make a whole that has the same shape. Or in patterns to make other shapes. Or even more variations, perhaps combining different fractal patterns. In my artwork, I have kind of cheated, because I use Photoshop warping to turn the image into what I want it to be, and the repeated shapes are no longer identical except for size. I put them with other pictures, I paint on them. I make them different. But they still fascinate me even when I alter them. They fit wonderfully with my kind of fantasy.
So Thank you, Benoit Mandelbrot. Perhaps in my simplicity I mis-understand your deep concepts, but thank you anyway, for being a scientist/mathematician who had an artistic vision that has enriched my life.