Chaos, Fractals, and Dynamic Systems

In the late 1980's there was an explosion of ideas in mathematics that just blew me away! It started with books like The Mathematical Tourist and Chaos. The PC was mature enough for anybody to experiment with nonlinear systems, and I was in heaven! Well, at that time, I was busy pursuing an engineering career and raising a family. But now in retirement, I have time to pursue some of these amazing ideas and share them with you.

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Iteration: "Play It Again Sam"

"Iteration" means to do the process over and over again until some desired result is achieved. We are going to have a lot of fun and discover some amazing things that result from the process of iteration.

Lesson 1: Introduction to Iteration (video)
Figure 1: Iteration Diagram (pdf)
Figure 2: Graphical Analysis (pdf)

Orbit Diagram for Qc = x*x + c
This simple quadratic equation has an amazingly complex orbit diagram for various starting (seed values) of c. For each seed value the orbit seems completely unpredictable, but it's pretty apparent there is an overall pattern. I have included the BASIC source code listing in the following article.

Orbit Diagram for x*x + c (pdf)
Zooming in on the Mandelbrot Set!
The Mandelbrot Set

The Mandelbrot Set is a beautiful and complex set of numbers! The closer you look, the more complex it gets! So, fasten your seat belts. We are going to zoom down into the depths of this amazing set.

Mandelbrot Zoom 1 (video)
Mandelbrot Zoom 2 (video)
There are thousands of wonderful books exploring the topics of Chaos and Fractals. Here are a few of my favorites:
Bibliography (pdf)