Broccoli can be something of an acquired taste, with children everywhere staging dinner-table standoffs with their parents over this dreaded veg. But whether you like the taste or not, it’s hard to argue with the aesthetic appeal of this particular variant – the Romanesco broccoli.
On closer inspection, the distinctive spiral is actually a repeating pattern. If you cut a piece off and zoom in, it looks exactly like the main head it originated from. Mathematicians call this a fractal, and this self-similar repeating feature can be see in everything from the formation of ice crystals on a frosty windowpane to the network of veins that provide nutrients in leaves.
Technically, the Romanesco broccoli is only an approximate fractal because, in the true mathematical use of the word, a fractal must repeat infinitely. For example, the classic Koch snowflake (below) is created by superimposing equilateral triangles on top of each other in very specific ways. When you repeat this process again and again, the resulting shape has an infinite distance around its edge, but a finite volume inside.
This all sounds delightfully trippy, and the resulting patterns are mesmerizing to look at, but what does this have to do with real life, other than providing you with an incredibly geeky factoid for your next social gathering?
In addition to finding these amazing structures in your refrigerator and on your windowpanes, the human body has them too. We are full of complicated structures and trying to model these with regular everyday shapes (spheres, cubes, etc.) is not going to be very successful. We need something a little more sophisticated than that, which has led scientists to apply fractal analysis to certain structures, such as the branching of the airways inside our lungs. A team of Japanese scientists recently used fractals to understand the complexity of small growths in the lung that were suspected of being cancerous. By combining this fractal math with standard imaging techniques, the ability to distinguish between malignant and benign was significantly improved.
So, the next time you’re in the produce section of your grocery store, reach for some Romanesco broccoli. Will it win over the kids? Maybe not. But it will give you a great dinner-table conversation starter!