On Beyond Chaos

Aloha! Welcome to my humble online abode! This is the home of my textbook, On Beyond Chaos.

I used this book for a math elective called Chaos Theory and Fractal Geometry at San Francisco University High School. The prerequisite for the course was precalculus.

The whole darn book is available for free as downloadable pdf files, although it's copyright ©2023 by Ben Jacobs. Creative Commons rules apply: Creative Commons License. This website contains the newest edition, which is being continually updated, revised, and (hopefully) improved.

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I’d like to acknowledge the students who suffered through the first draft of this textbook at San Francisco University High School during the fall semester of 2023. They helped me out immensely, and the book posted below is far better because of their input and feedback: Avery Fringer, Anika Gandhi, Angela Narkin, Jonas Rosenman, Andrew James, Arav Saksena, Eva Stuebe, and Nina Tashjian; thank you all so much! That said, any errors that remain in this book are mine and mine alone.

Here are some possibly useful links:

Here is a nice set of Java Applets for making orbit diagrams, from Robert Devaney and his team at Boston University: Orbit Diagrams. To run the Java applets on the Chrome browser I use the extension Cheerp J Applet runner. The Chaos Game is a nice Java applet as well; again I use Cheerp J Applet runner.
Here's a Julia Set program that uses Javascript: Julia Set Generator .
Here is a good online Geogebra app for making cobweb diagrams: Cobweb Plotter .
Here is a good online app for generating fractal shrubs: L-Systems Turtle Graphics
If you have any feedback or questions about this book, please let me know at ben_jacobs@yahoo.com.
If you're looking for my non-Euclidian Geometry textbook, click here.
Finally, if you're looking for my novel (or having trouble sleeping at night) click here.