Lorenz Attractor in 3D

Category: Chaos Theory
Published: Monday, 10 January 2011 02:32

Lorenz attractor is a fractal structure corresponding to the long-term behavior of the Lorenz oscillator. The Lorenz oscillator is a 3-dimensional dynamical system that exhibits chaotic flow, noted for its lemniscate shape. So this ting came out of the mind of the man who coined the term butterfly effect and one of the firs men who took chaos theory seriously. So lats look at the shape in 3D (WebGL).

delay r

Just press start;) You can play around with setting and rotate the object with mouse.

And why is Lorenz attractor so interesting? Lets just quote wiki: "Lorenz attractor is interest to the field of non-linear mathematics, the Lorenz model has important implications for climate and weather prediction. The model is an explicit statement that planetary and stellar atmospheres may exhibit a variety of quasi-periodic regimes that are, although fully deterministic, subject to abrupt and seemingly random change." And in plane words... It shows that even a simple model about the weather is susceptible to very small changes.

Now focus on the lower part of the graph. It sows us a projection of the 3D model in 3 planes. Does it seam familiar? Yes it is a time series and it looks similar to a time series of financial instrument following a sideways trend. Along the way I will explain why this is not an accident and what that means for us if we are interested in trading.