Fractals: the geometric code of nature

Hey there, welcome back!

Last entry we learned how to recognize different geometrical patterns in our daily live momentos and spaces. Now we will apply this perspective to nature.

A bit of historical background will be very useful for starters. That is to say the Pythagorean theorem, the formulas for calculating the surface and volume of different geometric figures, the number Pi... These are all concepts of classical or Euclidean geometry, which are taught in schools alongside analytical geometry (which translates these figures into algebraic expressions such as functions or equations) and which are perfectly adapted to the world we humans have created. 

But what if there were a "raw" geometry behind the behavioural patterns of the different elements of nature? A geometry not adapted to the world humans have created, but to everything that was here before they arrived, and even to the functioning of their own bodies. A new perspective with which to analyse and decipher the natural processes occurring around us: fractal geometry arrived (to stay) at the end of the last century.

The discovery of fractal geometry barely 50 years ago has made it possible to mathematically explore the "irregularities" of nature in many of its forms: What logic do the branches of a tree follow when they grow? Or the peaks of mountains, or even the path of lightning in a thunderstorm, the growth cycle of microbes or the formation of stars in the galaxy. All these natural phenomena can be decrypted thanks to fractal geometry.

                             

According to the mathematical principle of self-similarity the same shape repeats itself on a gradually smaller scale indefinitely, i.e. an identical shape within the previous one and so on. To infinity. Shapes, rhythms, sounds or trajectories, because all these phenomena can be decomposed into self-replicating structures, the main characteristic of fractals.

"Clouds are not spheres, mountains are not cones, coastlines are not circles and the bark of trees is not smooth, nor do rays travel in a straight line", said Benoit Mandelbrot, the mathematician responsible for coining the term fractal (from the Latin fractus, broken or fractured) in 1975. At that time Mandelbrot was working for IBM at the Thomas Watson Research Institute in New York after his time as a professor at several American universities. His task was to identify why white noise interference was occurring in the telecommunications system he was working on. Benoit Mandelbrot (1924-2010), born Polish and naturalised French and American in the context of World War II, had an exceptionally visual mind that enabled him to find the mathematical basis of fractals, despite the fact that these figures appeared irregular to the human eye. 

Have you ever noticed this before? What are your thoughts on this topic?