Interactive Sierpinski Triangle Fractal

After Lydia, one of my undergraduate students, completed her Math eNotebook on pennies I decided to use one of the ideas she had included as an interactive activitiy on the wall outside my office. The Sierpinski Triangle is an example of a fractal where each element is an exact copy of the whole, or vice versa.

Fractals are a wonderful example of how math is the science of pattern and how once you see the pattern the learning becomes much easier. The extra pennies on the left are for people to add to as they get to know the pattern and can predict where to place the additional pennies. Theoretically, this pattern could go on for ever although in reality it will probably stop when we either run out of room, or pennies. Here are some fractals in nature and here are some 'far-out' Mandlebrot fractals and MC Escher fractals.

You can also create your  simple fractal with this NCTM fractal tool or your own incredible fractal with this Nova interactive activity.