When Chaos is not Random

A short introduction to Strange Attractors

Or why the weather forecast is still wrong as often as it’s right.


Physicists at the turn of the century were struggling with what was then known as the three object problem.

One of the fundamental assumptions of science is that the world works in knowable, predictable ways. That if we understand the laws of nature and we know the necessary variables, we can predict anything.

The assumption works really well in the laboratory and on the theoretical level. The real world still defies science as often as not. This was the three body problem. Newtonian physics could predict how two bodies (Say a planet orbiting a sun) would interact but when they introduced three bodies (like a moon orbiting a planet orbiting a sun) things got really complicated really quick.

The three body problem was originally applied to astrophysics but it’s implications are much wider and ongoing. In fact, every field of science has it’s own version of the same dilemma. With each new development we get just a tiny bit better at predicting the results with a few controllable factors. But predicting the real world involves grappling with hundreds of factors and something known as the butterfly effect.

The butterfly effect was coined by mathematician Edward Lorenz, one of the founders of Chaos Theory. The butterfly effect has been grossly misunderstood by most as the notion that a butterfly flapping it’s wings in Brazil could create hurricanes in Texas. In actuality the butterfly effect is a fancy name for “sensitivity to initial conditions.”

Lorenz developed the theory while working on weather prediction models on early computers. He noticed that his prediction programs would be accurate for a short time, but small errors grew over time and they soon became a complete mess. He tried to enter the same data back into new models and got widely different results. Even tiny differences in the initial conditions (so tiny they could be compared to a butterfly flapping it’s wings) created significant differences down the line.

Because of this sensitivity, initially predictable results soon become chaotic, or random.

But they didn’t stay random. As computer technology and mathematical analysis grew, they discovered that if they continued to graph these theoretical systems, patterns emerged. The patterns often repeated themselves in fractals. They termed them strange attractors.

This is a simple Lorenz Attractor, named after Edward Lorenz. Chaos theory, like Quantum Theory, is filled with paradoxes. Individual events are predictable by science. But as those same factors continue to interact over time, they became impossible to predict. Given enough time, a pattern emerges that is, again, predictable.

Science Fiction master Isaac Asimov played with this notion in the Foundation trilogy. The creator of the Foundation, Hari Sheldon developed a science of psychohistory. His theory was that while the actions of a single individual was impossible to predict, the patterns of groups were, given sufficient information and time.

In my Galactic Consortium serial I am taking the same idea in a very different direction. Chaos theory, and especially fractal equations, have become popular with lay people because they make pretty pictures. There is a disconnect between what the graphs look like and what they really mean to scientist.

But what if there is a significance to their appearance as well? In the Galactic Consortium, the most advanced race, the Vatari believe so. The patterns of various equations (which appear everywhere in the natural world) are considered keys to a “divine language.” Understanding the symbols is key to understanding a level of physics that humans on earth have yet to develop, that of potentiality.


The Mandelbrot equation graphed.


Like the Mandelbrot, Barnsley is a mathematical equation turned into a graph.

How much truth is there to that idea? The Consortium is soft science fiction and I don’t intend to offer any proofs or arguments. But it does make an interesting idea for speculation. And some pretty cool artwork. Here are a handful of images I’ve created with GIMP and it’s built in Fractal Explorer. Nautilus Rose Fractal beauty of naturesun fractal green place




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