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.
