Fractals and complex numbers:
Big ideas
Each complex number (c) makes a new rule for how to make a Julia set. Finding the Julia set involves iterating a complex function (doing it over and over), and looking at whether the outputs stay small, or get very large. Numbers (z) that stay small when you iterate them are in the Julia set; numbers that get large when you iterate them are not in the Julia set.
If you look at each Julia set, and the number that makes its rule (c), then if the Julia set is connected, then that number (c) is in the Mandelbrot set. If the Julia set is in several pieces, then that number is not in the Mandelbrot set
Sample questions:
3. p. 477 # 12-15 See answers page for info about which of these I might put on a quiz
4. p. 478 # 16-17
5. p. 477 # 20-23
5b. another sample question (of the difficulty likely to appear on the quiz): Do 2 iterations of the function
z2+(-.5+.3i) starting with the number 0.