FRACTALS

by Sheila Connolly

A decade or more ago, I read a book from our local public library (which, BTW, had an extensive mystery collection) that I have never forgotten. Oh, I managed to forget both the author's name and the title of the book, but the gist of it struck a chord. I held on to only one word: fractals.

Benoit Mandelbrot 1924-2010

When I mentioned this over dinner one night recently, both my scientist husband and my literature-major daughter immediately said "Mandelbrot." After a little internet digging, it appears likely that the book in question was Benoit B. Mandelbrot's The Fractal Geometry of Nature (1982). Apparently Mandebrot created the term "fractal" in 1975, in an earlier work, and expanded his concept in the 1982 book. According to one source, he meant it to apply to "an object whose Hausdorff-Besicovitch dimension is greater than its topological dimension."

Uh-huh. The last math course I took was a summer school class in calculus, at a moldy high school somewhere in San Francisco around 1984, in preparation for applying to an MBA program. I understand about half the terms in that definition, including "is greater than."

So why did the memory of this book stay with me? I'm not sure why I pulled it off the library shelf, much less finished reading it, but I did. The single concept that struck me was the idea of self-similarity. To put it simply, as you zoom in on an image, from far to near, you will see the same pattern over and over, no matter what the scale. A view of a coastline seen from a satellite will have striking similarities to the distribution of sand grains on a beach in the photo, under a microscope.

This is a phenomenon found in a wide range of natural sources: sounds, blood vessels, trees (where the form of a branch is a replica of the whole).

All right, enough tech-speak. I freely admit I have only a shaky grasp on the concept. But what intrigued me was that there are patterns in the universe, many of which we didn't even know existed before the development of digital imaging, and they are internally consistent.

How does that relate to writing? Because for "pattern" you can substitute "style" or "voice." If you are familiar with a particular writer's style, at what level can you identify the writer? By a word, a sentence, a chapter? The whole book, the genre? That writer is unique, and his or her pattern should be too—and yet it fits into a broader universe of fiction writing. Think of contemporary computer programs that can analyze a document and, looking at the frequency of word use or the structure of sentences, can tell you if a manuscript was written by William Shakespeare. Can that be called a "fractal" application?

Or take it to the next step: if you wanted to forge a Shakespeare play, could you reverse the computer program and alter the structure of a play you had written to match his? With enough time and analysis, will we be able to reduce what we now label as "genius" to an algorithm? And is that a good thing or a bad thing?