The Maths Behind the Cauliflower Shape: Etienne Farcot, Assistant professor of Mathematics, at the University of Nottingham in the UK is stated to have cracked the maths behind how the cauliflowers take their ‘fractal’ shape.

In an article published in The Conversation the professor explains that the florets in the cauliflower

are similar and in maths, this property of self-similarity, which is a defining feature of abstract geometrical objects is called fractals. A new study, published in Science, has come up with an answer as to why they are similar.

Spirals are found in many plants, it is the main pattern of plant organisation – a topic that has been studied for well over 2,000 years. But although cauliflowers share spirals with most other plants, their self-similarity is unique.

About 12 years ago the professor along with his two colleges started, in France, François Parcy and Christophe Godin, started examining the florets, counting the spirals, measuring angles between them, studying the literature on the molecular mechanisms underlying the growth of cauliflowers, and trying to create realistic computational models of these mysterious cabbages.

If you manage to count the spirals, they will typically be numbers somewhere along the Fibonacci sequence, where the next number in the sequence is found by adding up the two numbers before it. This gives 0, 1, 1, 2, 3, 5, 8, 13, etc. On a typical cauliflower, expect to see five spirals going clockwise and eight anticlockwise, or vice-versa To understand how the geometry of plants develop over their lifetime, we need mathematics and microscopes.

We know now that for every plant, the main spiral is already formed at microscopic scales. This happens very early in its development. At this stage, it comprises spots, in which very specific genes are expressed (turned on). The genes expressed in a spot determine whether this spot will grow into a branch, a leaf, or a flower.

But the genes are actually interacting with each other, in complex “gene networks” – leading to specific genes being expressed in specific domains and at specific times. To work out how cauliflowers grow into their peculiar shape after the first few leaves have formed, a model which included two main components was built. These were a description of the spiral formation that we see in large cauliflowers, and a model of the underlying gene network that we see in Arabidopsis. What makes cauliflower so special is that these spots at the growing tip try to turn into flowers for some time (up to several hours), but keep failing at it for lack of “A”. Instead, they develop into stems, which turn into stems etc – multiplying almost infinitely without growing leaves, which gives rise to near-identical cauliflower buds.

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