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Dynamical Systems with Lorenz Attractors
Dynamical Systems with Lorenz Attractors
The Lorenz attractor is a nonlinear dynamic system that rose to fame in the early years of chaos theory. One of the most surprising features is its extraordinary sensitivity to initial conditions, a sensitivity that is not obvious when simply looking at the equations that define it. A minute fractional change in the initial conditions leads rapidly to a massive divergence in the path of the solution (popularized as "the butterfly effect"). The top graph shows two Lorenz attractors plotted with the same parameters except for the offset of the starting position. The bottom graph shows the length of the vector between the two solutions as a function of the curve parameter.