So, what does broccoli, clouds, trees, mountains or islands have in common? All of them exhibit a common property: fractality.
Think about a tree: branches and more branches… that’s a fractal! This property is called self-similarity! Leaves, galaxy clusters, plant roots, mountain ranges, the world wide web, etc… all those systems have the property that when you zoom in, you find the same structure, it’s the Droste Effect but translated into nature. (Visit Scale Invariance)
Now, a bit of history:
The term fractal, to describe such objects, was coined by the polish mathematician Benoit Mandelbrot from the Latin root for “fractured”. Mandelbrot used to give as an example the measure of Britain’s coastline because the same pattern is repeated again and again. Depending on the size of your ruler, you will obtain a different length.
Let’s try this with the Spanish Island of Mallorca (where IFISC is located)
When the ruler measures 30km, then the perimeter is 240km. However, if we shrink the ruler the perimeter changes! With a ruler of 15 km we obtain a coastline of 285km and 315 km for a ruler of 7.5km. The smaller the ruler, the longer the coastline is… But let’s go in depth in the study of the coastline.
As we zoom in the image, quickly we realize that the coastline’s shape is constantly repeated. For instance, the fact that there are details into details makes the perimeter impossible to be measured since we always need a smaller and a smaller ruler. This is the main property of fractals.