Fractals & Chaos Recap for 1/10

Download Fractal Zoomer.exe from here (don’t click the green button, that downloads something else). Use the navigation guidelines posted yesterday to help you use the program.

Play around with the program, but do so with intent. I have a few things I want you to explore:

  • Take unusual values of C from the Complex Paint worksheet and verify the connected/disconnectness of the corresponding Julia Set
  • Explore: Where in the Mandelbrot Set can we find values of C that correspond to area versus string Julia Sets?
  • Explore: What is the relationship between the location of C in the Mandelbrot Set and the orbit pattern within the corresponding Julia Set?
  • Challenge: We saw earlier that orbits of quadratics can contain up to Nine 6-cycles. Some are attracting, some are repelling, but most are complex. Can you find all nine of them in the Mandelbrot Set?

Also, if you’re interested in learning a bit more about three dimensional fractals, check out the game or information linked here.

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