A Look At Fractals: Sierpinski's Triangle

Use the slider in order to see the different iterations of Sierpinski's Triangle, a common fractal, where n=1 is the first iteration, n=2 is the second, etc. up to the sixth iteration.

1. After looking at the applet, what pattern do you recognize is forming?
2. From your response to question 1, and knowing that this applet depicts a fractal, how would you define a fractal?
3. What kind of equation/formula do you think you would use to model this phenomenon?


The beauty of this applet is it is easy to see how a fractal is formed and how it works. Through this applet people should be able to discover a fractal pattern and describe it. From there, it is easier to try and define a fractal in our own words. For instance, looking at this applet we can say that a fractal is a decreasing recursive pattern where the closer you look at a picture, or the more iterations you see, there is a pattern that gets more detailed and is similar to the patterns and iterations that came before. Even though it isn't specific in this applet, the third question allows the teacher to lead students into complex equations since they probably can't come up with an equation that would make this phenomenon occur with the math that they do know.

Alycia Jacobson, 15 November 2013, Created with GeoGebra