When I first saw the Mandelbrot set being computer generated, I nearly fainted. This was because of the intensity of connection with what I was observing. It was something profound and I had a visceral response to it. So having heard that Benoit Mandelbrot had died October 14th, I feel that I should mark his passing with a few words about the difference he has made to my understanding of life. Or try to anyway.
Wasn’t it Einstein who said that the most beautiful thing that we humans can experience is the mysterious? Well, locked inside the generated Mandelbrot set is something so mysterious it speaks of mandalas, hallucinations and maps of the psyche.
“What you ask is the beginning of it all ? And it is this…Existence that multiplied itself for the sheer delight of being. And plunged into numberless trillions of forms, so that it might…find itself…innumerably.” The words of Sri Aurobindo help to lead me to meet the Mandlebrot set on its own terms. The brain holds a wealth of symbols and many of them appear as if by magic from the computerised form of a simple equation that is made visible through an integrated feedback loop and the possibilities opened up by the computer age.
Mandelbrot was a mathematician employed by IBM in the late seventies, with the enlightened brief to play around with the new machines and see what he came up with. On March 1st 1980 he found something that would change the way we see the world for ever and ushered in the possibilities of a fractal universe. The key to this world lay in iteration-numbers flowing in two directions round and round in a loop, like a dog chasing its tail. The mathematician Julia had guessed at his sets but he couldn’t see them in action. Noone could, until the day when the astonished Mandelbrot watched his set come to life, seeing all the forms of energy emerging from a frontier that is infinitely complex, where each piece holds a miniature of itself and islands of order are created in a sea of chaos. Fragmented and irregular he watched as it took him up and out of the totality, without lines or circles but with a rhythm that the subconscious recognises. So the semaphore of nature was revealed and we are now able to witness how the physical world tells itself what it wants to be. The Mandelbrot Set ushered in a revolution in thought and a new mathematics to which Mandelbrot himself gave the name Fractal.
A fractal geometer can describe a cloud like an architect can describe a house. Under high magnification convoluted atomic landscapes appear and a mathematics was needed to describe them. The fractal world is one which simplicity and order at the root grows into something that contains infinity and the mystery of infinity.
What Mandelbrot’s extraordinary discovery points to is the fact that the human brain is the missing 5th element and that DNA is the ultimate fractal generator. It is like a new map leading us ever on to new treasures. They will lead to an unfolding within us.
One journeys into the Mandelbrot set and visits spirals within spirals, seahorses, whirlpools and so on. Every now and again a replica of the whole is buried within the boundary structure. The 2D set looks like a frilly double kidney with self same accoutrements but the point of it is multidimensional. It is an interesting thought that LSD and fractal geometry emerged historically in synchronicity. In deep structure we find the route to the mystery.
Some of the appeal of the fractal is that in each part lies the possibility of an image of the whole. That, to lost mankind, feels like a clue about the nature of existence. Although the Mandelbrot Set is only one of many fractals, it is the one that has most captured the cultural imagination of the world. It is the most popular self similar fractal generated by a recursively iterating formula. You can think of a fractal generator as working a lot like a MRI scan, which crosses over a patient’s body making a computer graphic representation of a 2D cross-section of a 3D object(the patient).
Fractal mathematics broke barriers imposed by standard Euclidean geometry. No wonder it grabbed my attention. Shapes and patterns believed to be random could perhaps be created by mathematical principles. This is still working through the system and shaking up the sciences. It is bringing the physical and the metaphysical close-too close for the comfort of some scientists. Just as there is a genetic code within us there could be a code for the universe and it could be a fractal equation. But we are unlikely to find it as we are not that clever yet. Best be content with the mystery and rejoice in the experience of being a part of the fractal revolution by letting our minds ‘go home’. Try it here.