Cavolo Romanesco: the “Math Cabbage”

This curious looking light-green vegetable that is popular in Italy is called a cavolo romanesco, also known as broccolo romanesco (“Roman cabbage/broccoli”), and it is not only tasty but naturally displays a few fascinating mathematical traits.

The humble cruciferous vegetable is a fractal, an object displaying self-similarity on all scales, creating a never-ending pattern.

More than that, the number of “peaks” on the cabbage is a Fibonacci number, and the peaks are arranged according to Fibonacci spirals. Fibonacci numbers are those that make up the Fibonacci sequence, that is, a sequence in which each number is the sum of the two preceding numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.

On the largest scale, the whole vegetable is made up of peaks lying in spiral patterns starting from the top. The number of spirals is also a Fibonacci number. Each peak looks like a mini cabbage in itself, in turn being made up of smaller peaks displaying the same entire pattern. In theory this would repeat to infinity, in reality the spirals and peaks get smaller and smaller until they reach the limit a physical object must reach.

The following image traces the spirals on one of the peaks. The clockwise spirals are red and the counter-clockwise spirals are black. There are 8 red spirals and 13 black ones, two consecutive numbers from the Fibonacci sequence.

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This next image gives a closer look at the repeating pattern.

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Simple and mind-boggling at the same time, Fibonacci spirals are often found in nature, from the famous nautilus shell to pine cones, sunflowers, certain animal bodies, hurricanes and entire spiral galaxies.

Just as importantly, the cavolo romanesco is also healthy and very tasty to eat, but “math cabbage” recipes are a post for another day.

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