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.