## Romanesco and the Golden Spiral

This week’s veggie box included the following beauty

The vegetable in the picture is called Romanesco. I’ve always thought of it as a cauliflower but I’ve more recently learned that it’s more closely related to broccoli. It doesn’t really matter because both broccoli and cauliflower are forms of brassica, which term also covers things like cabbages, kale and spinach. All are very high in vitamins and are also very tasty if cooked appropriately. Incidentally, the leaves of broccoli and cauliflower are perfectly edible (as are those of Romanesco) like those of cabbage, it’s just that we’re more used to eating the flower (or at least the bud).

A while ago, inspired by a piece in Physics World,  I wrote an item about  Romanesco, which points out that a “head” of Romanesco displays a form of self-similarity, in that each floret is a smaller version of the whole bud and also displays structures that are smaller versions of itself. That fractal behaviour is immediately obvious if you take a close look. Here’s a blow-up so you can see more clearly:

There is another remarkable aspect to the pattern of florets, in that they form an almost perfect golden spiral. This is a form of logarithmic spiral that grows every quarter-turn by a factor of the golden ratio:

$\phi = \frac{1+\sqrt{5}}{2}$.

Logarithmic, or at least approximately logarithmic, spirals occur naturally in a number of settings. Examples include spiral galaxies, various forms of shell, such as that of the nautilus and in the phenomenon of phyllotaxis in plant growth (of which Romanesco is a special case). It would seem that the reason for the occurrence of logarithmic spirals  in living creatures is that such a shape allows them to grow without any change in shape.

Although it is rather beautiful, the main attraction of Romanesco is that it is really delicious. It can be eaten like cauliflower (e.g. in a delicious variation of cauliflower cheese) but my favourite way of cooking it is to roast it with a bit of olive oil, lemon juice and garlic. Yum!

### One Response to “Romanesco and the Golden Spiral”

1. FYI Romanesco was also used in commissioning of the 3200 megapixel camera for LSST. I’ve lost the link to a piece from SLAC, but this was easy to turn up.
Vera Rubin: Super telescope’s giant camera spies broccoli
By Jonathan Amos
BBC Science Correspondent
8 September 2020
https://www.bbc.com/news/science-environment-54066586
Don’t be surprised that a lab more famous for particles and beamlines than astrophysics and cosmology is responsible. They are very much top-shelf instrument makers. There’s at least one tour of one of their machine shops (they operate several) on YouTube if anyone out there wants to channel their inner machinist.