To review what was accomplished previously in Chaos and Gaia, and to present other pictures of fractals with some accompanying explanations.

Pictures of fractals (enclosed), chalk board, quiz.

I Fractopia

II Review

III Quiz

I Fractopia

Present pictures of fractals (use various web resources or inlays).

Explain the role of complex elements (imaginary #'s) in the formulation of a Mandelbrot Set.

For example: i =, i^2 = -1, i^3 = -, i^4 =1 which creates a cyclic orbit as different degrees of i manifest. (An example is the Mandelbrot like set: Sinh1.000(Z)+C {Z = a + bi a, bZ}, use with applicable software if available).

II Review

Review the main points of the Chaos and Gaia lesson plans.

Go over home work quickly and then take questions from the class.

III Quiz (according to grading scheme needs)

1. Define the following: Chaos, Orbit, Iteration, Fractal, Self-Similarity.

2. Iterate the following function 3 times: a=1; b=1. f(x) = x (a + bi)^2 with the initial conditions x=1, 2, and 2i.

Note on assessment: This unit was a brief overview in some fractal mathematics. The assessment should be light and reflect what was exactly shown in the actual classroom session. If more or less material was covered you may want to alter the above quiz. Again this lesson was designed in the spirit of fun learning and the assessment should not be too rigid or demanding. Alter the above lesson and as desired. The next three lesson plans are more advanced by nature of the material and incorporate information from the chaos essays found elsewhere on this page.