Sensitive dependence on initial conditions in the Lorenz equations. The first coordinates of two solutions starting from (0.1, 5.0, 5.0) and (0.1, 5.0, 5.0001) are plotted with respect to time. Although the two solutions, plotted in blue and yellow, respectively, start very close, they diverge after about 17 time units, never to exhibit close behavior again. It is important to emphasize that these two solutions are computed with great precision and the sensitive dependence on initial conditions is not a numerical artifact; it is the hallmark of chaotic dynamics.

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