Lorenz in Living Color - Part 1: The Lorenz System

I've been working on a technology art project (not as cool as this one) for over a decade now and by "working" I mean "mostly not working".

The project got a started during the jolting transition from no-free-time college days to evenings-and-weekends-free life as a working engineer.  In the meager discretionary time during my college years I had read "Chaos: Making a New Science" by James Gleick and was captivated by chaotic systems.  The seed had been planted in middle school by the book and movie "Jurassic Park" and was nurtured by my physics professor into something that I could begin to understand.

And the quintessential chaos-exhibiting system was the Lorenz system, boring when expressed as a system of seemingly simple differential equations...

but compelling when plotted in space...

Each one of those green dots is a unique value of x, y, and z that satisfies those three equations.  And given any set of x, y, and z coordinates, those equations will determine where the next dot will be in a second or minute or year.  All these dots, this collection that defines the solution that appears over time, the math people decided to call the shape of these types of solutions "attractors".  The solutions to these equations swirl and combine yet never settle down into regular, predictable patterns.  Looking at the attractor from another angle makes this clearer..

There are two foci to the attractor, two black holes that the solutions swirl around but this view of the attractor shows the solutions move back and forth between the two lobes. Sometimes the solutions loop repeatedly on one side and sometimes they will switch and start swirling around the other.  We never know when a switch is going to happen and the paths never cross or intersect.  Looking at an animation of the solutions over time shows this best...


I found this all very intriguing in many ways.  Here was a simple system that acted infinitely, a set of equations that produced values that never repeated themselves yet clearly had structure and was much more than just random noise. The regular-but-not-repeatable pulled me in and I began to think of ways that I could try to express this, to show others just how interesting I found it.

x, y, z.

red, green, blue.

Each point in space on the Lorenz attractor could be represented by a unique color, a combination of varying amounts of red, green, and blue.

This was the kernel of the idea that started the project all those years ago.