Exploring the Fractal Universe

And now for something completely useless. Well, not completely, but for many of us, this subject will have no practical application at all - it's just fun. Fortunately, it's summer vacation. I think a little fun is allowed for most of us around now.

I have friends who are brainy scientific types. Over the last few decades, I was entranced by the stuff I saw lying around on their coffee tables. Books about the universe. Books about chaos theory. Books about fractals.

If you're not familiar with them, fractals are intricate, complex, mathematically generated patterns. The term was coined in 1975 by Benoit Mandelbrot. Merriam-Webster defines it as: "any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size."

As above, so below: when you zoom into a tiny corner of a fractal image, you see patterns that resemble the larger pattern you were looking at. Bubbles, ferns, dendrites, snowflakes....

I'm a lover of pattern, and to me fractals are utterly beautiful.

Those coffee table books with the glossy graphics were beyond my budget at the time, so I never had any fractal pictures of my own to get lost in. Recently my daughter, exploring the capacities of her PowerBook 3400, began playing with the graphing calculator. I explained the basics of graphing and how an equation turns into a line or a shape. She listened politely, but her attention was on the patterns. "Can you explain it later? Right now I just want to look!"

That reminded me of how I feel about fractals. Then I thought: Fractals! What better way to generate and experience them than with my iMac? I went to my favorite Mac download sites and typed "fractal" in the search boxes.

An embarrassment of riches awaited me. There are lots of fractal programs, most of them very compact and quick to download. All are interesting to work with, and some of the best ones are freeware. What more could one ask?

Imagine detailed graphing calculators in gypsy colors, dancing a fandango. These programs let you wander through the levels of various well known fractals - the Mandelbrot set, the Julia set - and many of them have larger selections, or let you write your own variations. Along the way they generate gorgeous graphics, one after another. PhoenIX records your tours of fractals as QuickTime movies.

Now when I have a little time and just want to indulge my love of fractals, I have only to open one of these programs. Among my personal favorites so far has been Fractal Explorer - it gives you many different options in fractal choice and zooming, and a wonderful array of display color sets. There's also Easy Fractal, Fractal Designer, Carbon Fractal, and lots of others. (Use Sherlock or Google to search for other fractal software.)

Fractals can be expressed in other ways. There's fractal music: Music composed using fractal structures. And so of course there are Web sites where you can view fractal graphics while listening to fractal music. If I keep surrounding myself with fractals, I may just turn into a fractal soon myself.

Next time you're in the mood to look at something just plain wonderful, open a fractal. No calories, but they may be habit-forming. Enough talking. I'm going to visit some fractals. See you there.