Thursday, 27 December 2012
Chaos- The Butterfly Effect
A butterfly flutters its wings in Guatemala and triggers a tornado in Guantanamo. While such stands as nothing short of a miracle, a perfect yet powerful expression of roll, pitch and yaw by a humble arachnid; it remains the metaphorical ideal for an entire dynamics bent on the eccentricities and capriciousness of nature. The bold and presumptuous notion that randomness is merely a mirage, that order and disorder are intimately linked and that small changes result in vast differences. The notion of chaos usually conjures the image of randomness and entropy whereas it is a manifestation of unpredictability and fluctuation played by the laws of nature. Everything from the emergent ethology of flocks of birds and the formation of the weather to the evolution of stock markets and economic crashes unveils a non-linear, irregular and unpredictable platform. One where the deterministic view collapses and makes room vacant for a chaotic framework of dynamically changing systems provoked by minute and seemingly trivial modifications. A double pendulum will assume a sporadic and capricious motion when released due to minuscule differences in the initial configuration, just as the weather varies due to fluctuations in atmospheric conditions such as convection as quantified by the Lorenz attractor. Chaos may be both observed and envisaged as a facet of nature; for mountains are not cones neither are clouds perfect spheres nor are trees flawless cylinders. It is the non-Euclidean geometry of the physical world that is addressed by the chaotic nature of fractals, essentially the byproducts of dynamically changing systems that convey a feedback loop of infinite regression, self-similarity and locally and globally oriented irregularity. Even simple contraptions such as a Poincare's three body astronomical system indicate that small errors in calculation result in chaotic subsequent outcomes, way out of proportion of the initial mathematical estimates and premises. Others such as the Belousov non-equilibrium thermodynamic reactions probe the chaos of chemical oscillation from a clear state to coloured to clear again; indicating a chemical basis of morphogenesis centred on the reaction-diffusion paradigm expounded by Turing. Chaos is kaleidoscopic; every small fluctuation, modification and variation constitute to the outcome and output. And however unpredictable, dubious and erratic that outcome may be, it is alway reducible to simplicity and lucidity regardless of whether its a Mandelbrot set or a Romanesco broccoli!