Natural Fractals

Among many, many others examples, we point out these. Click on the picture for a larger view.

The fractal structure of our lungs (picture courtesy of Dr. Ewald R. Weibel),
and fractal silhouettes of trees.

After using these and other examples to emphasize the differences between mathematical and natural fractals, I send students out to the web with instructions to find a picture of a natural fractal and describe why they think their example should be called a fractal. With permission, these can be posted to the course web page for everyone to examine and discuss. No longer are we limited to showing a selected few in class: the whole lot can be put on the web page, and even parts of the discussion can be done by posting to bulletin boards linked to the web page. Letting a topic percolate on the web for a few days can lead to a much more informed, and lively, discussion in class.

Some of these topics lead to deep questions, at a level of detail enabling thought-provoking class discussions. One of the best examples I have found is the fractal sutures of ammonites. Click on the picture to see the example.

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