The first strange attractor in history that was generated from computer simulations was Lorentz attractor. In early 60’s Edward Lorentz was tryning to simulate a model of flows in atmosphere based on a nonlinear dynamical system.
He noticed that although some solutions are extremely complicated, they remain bounded on a region of phase space, which is called Lorentz attractor…
However, his huge contribution was that these solutions were extremely sensitive to initial conditions. This sensitivity is considered to be the fingerprint of chaos and chaotic solutions when they appear in nonlinear dynamical systems.
The above figures are different orbits of Lorentz system that are being ‘unfolded’ in Lorentz attractor. These solutions for every instant define a point on phase space, and successive points form the orbit of the system. Different values in parameters define different solutions and so we get different orbits… and some of them are chaotic.
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