They will watch Life by the Numbers video, Patterns of Geometry, program segment four, New Geometry, in order to develop a deeper understanding of how we can duplicate nature's patterns by using math and iteration of self-similar mathematical elements. After the video, the class will break into groups of two. This exercise will lead them to make connections between the iteration process and exponentially increasing data. Today and over the next two days, the students in their groups will also do two online exercises. The first is a simple square construction that is divided with diagonals.
Iteration is performed on the square dividing it up into smaller and smaller self-similar triangles.
The square can be opened demonstrating in a striking manner the birth of a fractal from iteration. The second construction will allow the students to construct a Koch snowflake and design their own fractals. They will turn in one design, with observations about it, and an analysis of what small changes in the initial conditions of their fractal can do to the end product. On day two of the lesson, the students will play the Chaos Game. This will lead them to recognition of the order present even in random processes.