A Delicious Fractal

romanesque cauliflower

A small Romanesque Cauliflower. (Click for larger view.)

Imagine my delight when I spotted this lovely piece of edible mathematics in the Hollywood Farmer’s Market this morning. The stall has several of them of many sizes (this was a very little one) and of several colours. Wonderful. If you don’t know what I mean when I talk about the mathematics, or use the term fractal, look it up. There are several things of note, among which are the wonderful spiral structures that you can see (Fibonacci spirals) all over, and which in various ways, encode the infinite sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…. (you get the next one by adding the previous two) called the Fibonacci sequence. Ratios of successive members of the sequence, (e.g., 5/8, 8/13, 144/233, etc) approximate what I’ve already mentioned in an earlier post is definitely my favourite number (if I have to pick one), the Golden Ratio (or Golden Mean): (\sqrt{5}+1)/2\simeq 1.61803\ldots which is also embedded in the spiral. Next there’s the fractal nature of the structure. Each of those little florets of the vegetable/flower is a little microcosm of the entire structure. There are little spirals on it and so forth, arranged in the same way. Next, you can find a little set of florets on the florets, which also is a microcosm… and so it goes on…

Here are two more shots of the same, from different angles. Click for larger views to see the wonderful structure.

   romanesque cauliflower   romanesque cauliflower

Guess what? Like yesterday I have a beautiful tasty thing that I can’t bring myself to eat!

-cvj

Some Related Asymptotia Posts (not exhaustive):

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