Benoit Mandelbrot was a man concerned with chaos. His vision as a mathematician was to master the complexity of an unknown order of disorder. He looked at his world and sought to find a rule that might explain the unexplainable in nature. What he achieved was a simple equation tied to a simple idea, the products of which are capable of achieving a complexity that reaches the unbounded limits of infinity.
His work gives an insight into the totality of a developing world of complexity. It allows us to apply geometry as a metascience, choosing to ignore the intricacies of experience in favour of a vista so monumental that it cannot be described. Scientists have theorised that the work behind the Mandelbrot set might lead us to some way in understanding so much of the universe we inhabit. But is there truth in the idea that Mandelbrot might have managed to capture the thumbprint of god?
It’s undeniable that Mandelbrot’s image provides a reflection on the aesthetic of so many of nature’s structures. It gives a viewpoint into exponential growth in unfolding time, its inception providing images reminiscent of the branching tributaries of the amazon or the reaching dendrites of a neuron. Under specific instruction its function can be programmed exactly to reproduce the nodules of a cauliflower or the peak of a mountain top. It appears that in his work Mandelbrot stumbled across one of the fundamental driving forces of nature, but can anything of meaning be inferred by aesthetic associations?
The Set is a geometric, visual representation of a quadratic equation under the drive of reiteration. It is a mathematical visualisation of the mastery of maths over chaos. Mandelbrot used the basic principal of repetition on a large scale, reiterating his equation, to achieve something vast out of something that uses mathematics as simple as addition and multiplication. He found that by the process of reiteration he could draw order from a system that was previously unfathomably complex. With the use of powerful computers Mandelbrot was able to visualise his ideas, giving a series of images called fractals; the most important being the original: the Mandelbrot set.
Although visually stunning, it has been difficult to find an implied conclusion from the work of Benoit Mandelbrot. Since its inception in the 1980s the science has been used for applications on a wide ranging scale from compression of satellite signals and high definition digital imaging to medical technology relating to its observability in the human form. The most interesting aspect of these fractals come from their unproven but striking resonances in human culture. Both Buddhism and Hinduism, for example, use the Mandala: an intricate, circular image to focus the spiritual self (see above image). Although ancient and derived from the creativity of spirituality, the Mandala takes the form of a Mandelbrot fractal. It might be interesting to examine this as an intersection of science and religion, achieving the same goal by differing means.
Professor Ian Stewart of the University of Warwick, believes that the Mandelbrot set can give us an insight into the deterministic nature of our world. “It has previously been thought that chance and determinism are incompatible. The Mandelbrot set and chaos have proven that we can have both at the same time. It is no longer whether God plays dice that matters, but how God plays dice.”