The Fractal Shape Of Cauliflower

Cauliflower is quite popular right now.  You can find it riced and served instead of rice, used as the dough of pizza, and in so many other ways but mathematically, it is a fractal and someone finally figured out how to explain it's fractal shape.  

First of all, if you look at the cauliflower carefully, you'll notice that many florets look like miniature versions of themselves while looking so much alike.  This is called self-similarity which is one of the properties of fractals.  Furthermore, cauliflowers show a high level of self-similarity, often seven or more copies of the same "bud".

All califlower but most especially romanesco cauliflower show spiraling pyramidal buds as shown in the picture. Bud after bud, spiraling endlessly around. The spirals follow the fibonacci series of 0,1, 1,2,3,5,8....... and in the cauliflower there are 5 spirals clockwise and 8 counterclockwise or vise versa.

Now the question is "Why does this happen"?. Well it turns out the answer is based in science. It was discovered that the main spiral begins at the microscopic level extremely early in its development. The genes work together to form gene networks that are beyond simple intuition and mathematicians rely on differential equations to predict the the gene networks behavior.

People made a model to see how cauliflower grew into their unique shape after the first few leaves show up. The model was based off of two things. First is the spiral formation of the cauliflower and second is the gene network seen in plant Arabidopsis because this plant has it's own version of a cauliflower due to a one pair gene mutation.  

In addition, Arabidopsis is related to the cabbage family and cauliflower.  There is a lot of data available on this plant since it has been studied extensively which gave mathematicians some basic information. They discovered that there are four genes involved in the development of cauliflowers are S, A, L, and T.  In the Arabidopsis, the A is missing in the parts that become like a cauliflower and it is the gene that causes parts to become flower. It appears the lack of A is what causes the buds in the cauliflower making it look as it does.

The model used actually produced a visual result similar to the cauliflower. Due to the lack of the A gene, the cauliflower attempts to make a flower but instead they develop into stems, after stems, after stem with the same angles between each. This is cool that people can now explain how the cauliflower is a fractal.  Let me know what you think, I'd love to hear.  Have a great day.