What's that? You say you're hearing about fractals and chaos all over the place, but still aren't too sure what they are? How about a quick summary of some key concepts:

1. Even the simplest systems become deeply complex and richly beautiful when a process is iterated over and over, using the results of each step as the starting point of the next. This is how Nature creates a magnificently detailed 300-foot redwood tree from a seed the size of your fingernail.

2. Most iterated systems are easily simulated on computers, but only a few are predictable and controllable. Why? Because a tiny influence, like a "butterfly flapping it's wings," can be strangely amplified to have major consequences such as completely changing tomorrow's weather in a distant part of the world.

3. Fractals can be magnified forever without loss of detail, so mathematics that relies on straight lines is useless with them. However, they give us a new concept called fractal dimension which can measure the texture and complexity of anything from coastlines to storm clouds.

4. While fractals win prizes at graphics shows, their chaotic patterns pop up in every branch of science. Physicists find beautiful artwork coming out of their plotters. Strange attractors with fractal turbulence appear in celestial mechanics. Biologists diagnose dynamical diseases when fractal rhythms fall out of sync. Even pure mathematicians go on tour with dazzling videos of their research.

Think all these folks may be on to something?