Sage Interact: Chaos Game

A friend of mine sent me a link to the video "Sequences 10: Fractals and Chaos" which begins with a very clear explanation of iterated functions before introducing the Chaos Game. The video was well crafted but when the presenter wanted to "fast forward" through the Chaos Game he resorted to using a graphing calculator. There wasn't anything particularly bad about that, but certainly Sage will do a much better job than a graphing calculator. I've created a Sage Interact manipulative to demonstrate the Chaos game in a way that complements the video.

Although I've shown you 10,000 iterations above, running it in 'line' mode took over a minute so I decreased the maximum number of iterations for the version I posted. You'll have to play around with it to find a number that works well for your system. The output is posted on the Sage Output page and the Sage Code is posted on the Python/Sage page. Remember, even if you don't have Sage installed on your computer, you can quickly run the code on the Sage Cell Server; just copy, paste, and press 'Evaluate'.

If you've got a flipped classroom then the video provides a great introduction to the theory that your class can view at home while the Sage Interact manipulative can give them a chance to experiment on there own. Now if I could just teach a class that lets me use these resources....

I liked the video well enough that I clicked around to get his full list of videos here; the videos cover a variety of topics such as the distributive property, calculus, trigonometry, and even study skills. The videos are a nice resource, but it's seeing demonstrations like the Chaos Game that can capture the attention of a class more than any textbook.

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