The new short story I drafted this month has a brief description of something that resembles the “strange attractors” from Chaos theory, so I spent a little time refreshing my memory about Chaos. In the most general and oversimplified terms, Chaos theory is a study of how apparently orderly systems give rise to apparent disorder, and vice versa. It also involves fractals, which are fun, and they give insights into how very simple sets of rules can create enormous complexity.
My introduction to Chaos was the 1988 book Chaos: Making a New Science by James Gleick. Along with Stephen Hawking’s A Brief History of Time, which came out the same year, I read it in 1989 or 90 when I was still in high school, and it blew my mind. It isn’t a mathematical textbook but a history of the pioneers in the field and their discoveries. It lays out the basic concepts in layman’s terms and how they apply to a vast array of disciplines that study dynamic systems, from the weather and animal populations to the human body and your heartbeats. It also has a lot to say about how a revolutionary, interdisciplinary field at first met with apathy or outright resistance from the scientific establishment.
If you don’t have the time to read the whole book, you can get a brief but engaging introduction to some of the concepts in the following video from Veritasium.
A few years after Gleick’s book made inroads into popularizing the topic with general audiences, Chaos reached the masses through the first Jurassic Park film, based on Michael Crichton’s exceptionally entertaining 1990 novel. You’d be hard-pressed to find someone from my generation who isn’t familiar with Jeff Goldblum’s performance as Ian Malcom and his famous line, “Life, uh, finds a way.” On the other hand, the film didn’t do much to explain real concepts of Chaos, and probably left people with the impression that it just means “Things can and will go very wrong, very quickly.”
That’s not so much Chaos theory as it is Murphy’s Law, but whatever. Science-fiction stories are notorious for latching on to the smallest shred of a “sciencey” concept and turning it into a fantastical plot device. I’ve written before about how the term “science fantasy” seems more accurate to me, despite being outdated. From piloting spaceships through wormholes, to nanobots that can magically do anything, sci-fi is mostly bunk science: a fantasy about something science-related.
I’m as guilty as any SF author in that regard, but I did want my current story to do justice to this one bit of Chaos. The characters encounter a phenomenon that at first seems wildly unpredictable; but upon closer examination, a type of order appears. While movement is unpredictable at any individual moment, the totality of the movement falls within certain boundaries or parameters.
That’s the oversimplified idea behind strange attractors such as the Lorenz attractor, which is usually shown as a two- or three-dimensional graph that helps us visualize the possibilities for a set of three non-linear equations developed by Edward Lorenz, one of the Chaos pioneers who was originally trying to use computers to model weather systems. While the solutions (or iterations) never repeat themselves exactly, the graph helps us see that they all take place within a certain “shape”.
Anyway, there isn’t much of a point to this post, except that Chaos is fun to learn about! For engaging introductions to the Chaos-related concepts of fractals, see the following two videos.
Benoit Mandelbrot briefly discusses fractals and the art of roughness:
Dr. Holly Krieger explains the math of the Mandelbrot Set pretty simply: