Wednesday, 27 May 2020

Lockdown Day 65 - Fractal Cauliflowers!

Although we haven't grown any Romanesco Cauliflowers this year, we have done so in the past.

As we both did degrees in Mathematics, we refer to them as "Fractal Cauliflowers". Now, for those of you that aren't familiar with the term "fractal" let me explain. A fractal is a design or shape or object that is "self similar" on every scale, in other words if you see an image of an object then zoom in, you see the same image repeated at smaller and smaller scales.


If you look at the picture above of the Romanesco Cauliflower we grew a few years ago, you will see that if you zoom in you will see little minature versions of the cauliflower making up the whole head.


Zoom in further and you see that these are in fact made up of ever smaller cauliflower shapes, repeating like this until you can't see any smaller.

At university I wrote a program based on generating the Koch Snowflake but expanded this program to include starting with 4 and 12 sided shapes. Starting with a 5 sided shape produced something like a fractal version of the Olympic Rings and a 12 sided shape produced a fractal version of a daisy chain necklace. In real life, a coastline is an example of a shape which, if you look at it in smaller and smaller chunks, increases its length continually, but where the total area enclosed is finite. One day I will have to try and program up a cauliflower shape on the computer!

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