The part of the broccoli that we typically eat — what we call the head — is actually the flower bud of the plant (although broccoli leaves are just as edible and delicious, and can be cooked like any other green). The tight clusters that form the head are called florets (or small flowers).
On a Romanesco, the whole head is made up of smaller heads that mimic the shape of the larger head, and each of those smaller heads is made up of even smaller, similar heads. It keeps going, and going, and going…
You’re looking at a natural fractal — quite simply, a detailed pattern that repeats itself ad infinitum. (But since a head of broccoli can’t go on forever, math purists would call this an approximate fractal, since it has a termination point.) If you break off a floret, it looks like a mini broccoli with its own mini florets.
If you ever have the chance to study a tight head of Romanesco up close, you’ll see a spiral emanating from the center point, along which all the smaller florets are arranged. This is the Fibonacci spiral, a series of arcs whose radii follow the Fibonacci sequence.
If you count the number of spirals in one direction, and then count the number of spirals in the other direction, they will be — without fail — consecutive Fibonacci numbers. Every time.