Fractals: The Math of Ferns
Martha Torstenson, Math Teaching Fellow

This week in math class, we took a break from our computers to think about fractals and the way that these beautiful mathematical objects appear in the natural world. We began by learning what fractals are. We looked at some classic fractals including Sierpinski’s triangle and the Koch snowflake and discussed the pattern of self-similarity at multiple scales that they exhibit. We also touched briefly on the fact that these objects can be thought of as having 
Fractional dimension. We noted that these kinds of patterns are visible all around us, in the shapes of cumulus clouds, the branching of trees, the curve of a coastline and in ferns, which are plentiful at Conserve School.

To explore this concept for ourselves, we went outside to measure the length of the edge of a fern. In pairs, the students measured the side length of a fern at three different levels of fine-ness. The most fine scale seemed like it was going to take a long time to measure, so we used our knowledge of fractions to make an educated guess! We found that the length of the side of a fern depends greatly on the scale at which you measure it. When we went back inside to discuss our findings, we noted how our experiment relates to the “coastline paradox”. It was fun to think about how we can use math to think about the patterns we see all around us as we walk through the woods.

Students measuring ferns
Math students measuring ferns
Using fractals to measure ferns

Photos contributed by Caitlin Lemley, Math Teacher