## Romanesco and the Golden Spiral

Posted in mathematics, The Universe and Stuff with tags , , , on October 7, 2021 by telescoper

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!

## Romanesco and the Golden Spiral

Posted in mathematics, The Universe and Stuff with tags , , , on November 8, 2016 by telescoper

Some time ago I mentioned that I received one of these in my weekly veggie box..

Actually, that reminds me that a new box is due tomorrow morning…

Anyway, 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).

It turns out that this week’s Physics World has a short piece on Romanesco, which points out that a “head” of Romanesco has 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:

However, one thing that I hadn’t noticed before is that 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.

Not really relevant to anything much, I know, but I thought you might be interested…

P.S. One thing the Physics World piece fails to mention is that, regardless of its geometrical properties, Romanesco is really delicious!

## Variations on the Theme of Vegetables

Posted in Biographical with tags , , , , , , on October 7, 2016 by telescoper

When at school I had an English teacher who encouraged us to practice writing skills through a series of exercises that required us to write a piece that successfully connected two different events or ideas. I found those exercises very useful and I sometimes try the same thing when I’m stuck for something to write about on this blog. So here’s a hamfisted attempt to shoehorn two things that happened this week into one blog post.

One of the first things I did when I moved back to Cardiff in the summer was to reinstate weekly deliveries of fresh organically-gown vegetables direct from a farm via a company called Riverford. I blogged about the the reasons for doing this some years ago, including the following:

I have a standing order for a small box of vegetables every week costing about £10. The composition varies from week to week and with the time of year. The company does email and post on its website the contents of the following week’s boxes, but I generally don’t look at it. When the box arrives, it’s usually a mixture of staples (potatoes, carrots, onions, etc) plus things that are not so familiar, and often things that I’ve often never cooked before.  If it hadn’t been for the veggie box, I would probably never have found out about how to cook chard, romanesco, jerusalem artichokes and celeriac. I look forward to these surprises. Not knowing exactly what’s coming forces me to cook new things, and if I don’t know how to cook them there’s always google.

Here’s an example here from this week’s box:

This extraordinary fractal object is Romanesco. It’s obviously related to the cauliflower, but has a much firmer texture and has a distinctive “nutty” flavour. I am looking forward to cooking and eating this at the weekend!

Another reason for resuming the veggie box service (still only £10, by the way) is that I’ve had medical advice to increase my consumption of fresh vegetables, especially those rich in Vitamin K (which includes the various Brassica that includes Romanesco, but also cabbages, broccoli, kale, spinach, chard and a host of other things that I really enjoy eating anyway.

This brings me to another topic that has been on my mind this week. A chance conversation with a friend who happens to be a GP revealed that she’s seen a worrying upturn in the number of (male) university students presenting with symptoms of scurvy, an extremely unpleasant and potentially life-threatening condition caused by a deficiency of Vitamin C. University students are not famed for their healthy eating habits, and the prevalence of fast-food outlets combined with inadequate knowledge of even basic cooking techniques among young men is probably responsible for this regrettable phenomenon. The human body is not able to make its own Vitamin C so we have to make sure we eat enough food containing it. However, the recommended daily intake is actually rather small and is easily met by a modest intake of fruit and vegetables. Sailors on a diet of hard tack and salt pork had an excuse for developing scurvy, but there’s no reason at all for anyone – even students – to suffer the same fate by living on crisps and kebabs.

Anyway, if you work in a university I hope you’ll consider passing this advice onto your students. Indeed if you’re at a proper university that still does small-group teaching in tutorials, why not offer your students some fresh fruit or orange juice? Just a thought.