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PEERING INTO THE NATURE OF OUR MATHEMATICAL AND GEOMETRICAL UNIVERSE

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

Ignacio

PhotoFunia TV interference Regular 2014-08-04 01 55 05

©2021 by Ignacio Alperin Bruvera

Ignacio Alperin Art
http://www.ignacioalperin.com
http://www.theartofthinkingoutloud.com

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By Ignacio Alperin Bruvera

Ignacio Alperin nació en Argentina, creció en Australia y vivió temporariamente en varios países alrededor del mundo. Es un creativo en la definición más amplia de la palabra. Posee una experiencia internacional extensa y diversa, obtenida en una carrera profesional alejada de lo lineal. Hoy en día es Profesor en los MBAs de la Universidad Católica Argentina (UCA), Profesor de Creatividad e Innovación (Grado) en UCA Internacional y da clases y charlas como profesor visitante en entidades extrajeras. Es un emprendedor serial, aparte de consultor en temas tan variados como creatividad, innovación, liderazgo, arte y todo tipos de temas relacionados con el management y la dirección de empresas. Es también orador en eventos nacionales e internacionales, escribe ocasionalmente en diferentes publicaciones y por supuesto, tiene una carrera establecida como pintor y artista plástico.

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Ignacio Alperin was born in Argentina, grew up in Australia and lived temporarily in several countries around the world. He is a creative in every possible description of the word. He has an extensive and diverse international experience, obtained in a professional and corporate career far from the linear. Nowadays he is a Professor in the MBAs of the Argentine Catholic University (UCA), Professor of Creativity and Innovation (Degree) in UCA International, and gives lectures and talks in foreign universities. He is a serial entrepreneur, and a consultant in such diverse areas as creativity, innovation, art, leadership, and other management and business related subjects. He is also a key note speaker in national and international events, he occasionally writes for different publications, and of course, he has a well established career as a painter and an artist.

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