Another striking characteristic is that the shapes embedded in the fractal patterns can reappear at smaller and smaller scales. Some striking features of fractals include their remarkable similarity with patterns found in nature such as the crystal shapes of snowflakes, or the patterns in a fern frond. The attractors of chaotic systems are called ‘strange attractors’.Īt the time that René Thom (1923–2002) was developing the related ‘catastrophe theory’, a French mathematician Benoît Mandelbrot (born 1924) developed a geometric representation of everything from natural phenomena to the strange attractors of chaos, using ‘fractal geometry’. Once the movement is represented or mapped on the coordinates, a pattern appears. A simple pendulum swing would have a two-dimensional phase space of velocity and angle. This map or depiction would be called a phase space, corresponding to the coordinates of the movement. Chaos mathematicians in the 1960s would map the trajectories, for example, of a simple pendulum. Therefore a slight change in the initial condition could have a vast impact on the outcome, as exemplified by the ‘butterfly effect’ and in the work of meteorologist, Edward Lorenz (born in 1917).Īdvances in chaos theory and its mathematics are owed to physicist and mathematician Jules Henri Poincare (1854–1912), who used topological techniques to visualize mathematics. Chaotic systems are characteristically sensitive to initial conditions. Examples of chaotic systems include the behavior of a waft of smoke or ocean turbulence. ![]() ![]() For example, unlike the behavior of a pendulum, which adheres to a predictable pattern a chaotic system does not settle into a predictable pattern due to its nonlinear processes. von Schilling, in International Encyclopedia of Human Geography, 2009 Chaos TheoryĬhaos theory describes the qualities of the point at which stability moves to instability or order moves to disorder.
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