Mandelbrot is popularly known for two things in particular. Fractals, a description created by him to explain the nature of the sets he had discovered, and the Mandelbrot set. A simple iterated equation based on only sums and multiplications which, with the use of computers given its complexity, we were able to find that it created ever repeating and closely related patterns that could be larger than the whole universe within their own restrictions.
A simple explanation would be that all numbers that exist outside the set are there, but the set within its own boundaries can grow to infinity. I know it is difficult to rap one’s mind around it, but once you see it graphically it all makes sense. Some people have ventured that since there is such a mathematical bases for everything in the Universe, maybe “God’s equation” of creation may look something like the Mandelbrot set.
Leaving aside metaphysical considerations, and for those who have not heard of the set and fractals before, I will try to give you a simple and tasty explanation that may make some basic sense, before we delve into the documentary.
I use this example in class very often to show that things are not necessarily following what we call “obvious patterns”, or “common sense” explanations. It is also a very simple visual tool to show the nature of fractals. Basically it attempts to explain how from a finite object, and without changing most of its basic characteristics or those around it, we can derive into an infinite set.
Basically I take any pound square cake (the use of a cake allows everybody to have a piece at the end! 🙂 ). It weighs a pound, and its length, lets say for argument´s sake, is of 30 cm. We half it and we put one half on top of each the other (we add height but we do not change the total length nor the weight). We half again and put it on top, and so we go on and on. The idea is to graphically show how I could build an infinite cake -in height at least- from a finite one in length (which added will always remain the same if no crumbs were lost) and weight. If I had the right tools, instead of a simple knife, we could go into slices in microns, and even further, as we keep dividing and piling up ad infinitum. That is how we get infinite height from a finite and well defined object.
The documentary I have found, which is a remix someone has made from several documentaries that are available online, will explain in very simple terms the nature of the Mandelbrot Set and fractals. For artists like myself, it is of great interest as it reveals patterns from nature and the Universe that can be replicated as artistic creations, but the set -obviously- goes way beyond such a menial use. In fact it may give us a glimpse of how the universe may be structured.
I hope you see it and enjoy “The Mandelbrot Set”.
Until next time
©2021 by Ignacio Alperin Bruvera