math 2013
Shodor > SUCCEED > Workshops > Archive > math 2013

Today, Jenny started the workshop by introducing the students to the "Hilbert Curve". The "Hilbert Curve" is an example of a fractal - a pattern that kept repeating and that generally kept getting more complex as there were more iterations were done. The class then saw that at some point, the "Hilbert Curve" formed a solid diamond. The fractal filled up an entire two dimensional space. The students were also introduced to the "Koch's Snowflake". The instructor showed the students how the perimeter of the figure kept growing larger, going towards infinity, yet the area of "Koch's Snowflake" was still quite finite.

The students then explored other fractals, and learned that with some of the fractals that they saw, they are neither one dimensional or two dimensional. Somewhat unusual much like how "Koch's Snowflake" had an infinite perimeter, these had a bound area. Afterward, the students finished the lesson with "Julia Sets" and the "Mandelbrot Set". Next, the class explored some unique properties of the "Mandelbrot Set", like how it was possible to do simple arithmetic with it, or how in certain parts of the "Mandelbrot Set", it repeated itself.