Most people have probably never heard of Benoit Mandelbrot, but, they are much more likely to have had someone describe an image or object using the word ‘fractal’. Before the early 1970s when he would release his groundbreaking ‘The Fractal Geometry of Nature’, he was busy surviving WWII and finding his way through academia. Being Jewish and living in France at the time, his family moved out of Paris into the country where Benoit continued his studies with a local Rabbi. This period was fraught with fear of the Nazis, but when the war ended he was able to go back to Paris and attend regular studies. His education was long and complex, going from France to America, being involved at several institutions, and working for IBM, during all of which he developed a new system of how to look at nature, the world, the universe, and basically everything.
Geometry has been around since approximately the middle of the 4th century BCE, under the specific system created by Euclid. Since then, most work in geometry has built upon the Euclidean model, which we still learn today in school. There have been some advances away from it but there was never really a full break towards a totally new understanding of objects and the potential mathematics to describe them, like in so many other sciences. This only really came when Benoit Mandelbrot tried to understand why so many objects in nature did not resemble squares or circles or triangles.
From the introduction to his groundbreaking work, he explains, “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line” but all of these have regular, consistent structural patterns, that are everywhere on the planet. These never take on the perfect shapes described in Euclid’s geometry. In this partially irregular partially constant perception of the natural world, Benoit discovered something incredible.
Having access to computers through his time working for IBM, he was able to attempt simulations of potential geometrical patterns which he saw everywhere around him. These became what he termed ‘Mandelbrot Sets’ and here the first images were made which have become a widespread visualization that many people would instantly recognize.
In the simplest explanation, what he proposed was a self-replicating program which in its replication would produce smaller and smaller versions of the original, moving towards intricate and infinite complexities. For instance, a tree trunk becomes two smaller trunks called branches, these two become four, and so on, until the size of the branches get so small that leaves start to form, which are networks of tinier branches themselves.
Nowadays, the implications of these ‘fractals’ are everywhere. More recently in 2010 Stephen Wolfram spoke at a TED talk about his own ‘New Science’ which is based on programming language. He admits that his project is definitely inspired and influenced by the theories of Benoit Mandlebrot, and what he is working towards might be able to explain the underlying physics of the whole universe. What is fascinating about Benoit is the kind of humble temperament he had in pursuing this unique and often dismissed perspective on a vision of nature. It is important to consider that some of the most far-reaching scientific revolutions have begun with a simple, humble perspective, of someone who doesn’t necessarily fit in with the traditional methodologies or perceptions of the world.
Maybe if more of us held on to our strange or weird ideas about life, in the face of accepted traditional models, there would be more opportunity to discover the unlimited potential in scientific observation and potential technology. Though in pursuing this, like all those great revolutionary thinkers of the past, for a time, we might become scapegoats, outcasts, and even heretics. Here we would be standing on the shoulders of such people as Benoit Mandelbrot, and probably be a little closer to reaching into space and touching the stars.
Author: Jonathan M. Bessette