Today's class explored fractals using several different applications. They first went to the interactivate site about Sierpinski's Triangle. Then they used Geometer's Sketchpad to write a script that would create the traingle. After using some premade scripts to see some more fractals, the students went on break.

After break, the class resumed with a sequence that the students had to solve. Using a spreadsheet, they found the pattern: n ² + c. Bethany explained that different starting numbers would create different patterns: converging, diverging, and repeating. If a number's sequence diverged, it "escapes" to infinity, but if it repeats, it is a "prisonner" to the sequence. Some numbers must be put through the sequence for a very long time until its fate can be determined, and this is what makes the sequence so interesting. The students learned about a famous fractal called the Mandelbrot set that used a variation of the sequence, and then they got to explore the set on the Interactivate site. They found that the set actually contains repetitions of its shape on the fringes of the "prisonner" and "escapee" numbers.