This animation, created using MATLAB, illustrates two "chaotic" solutions to the Lorenz system of ODE's. The trajectories are shown to the left, and the x solutions are shown to the upper right as functions of time. The absolute difference between the two are shown to the lower right. The viewer should observe that there is seemingly no difference (due to nearly identical initial conditions) between the trajectories for time less than 20. The difference is made plain for times greater than 25. The trajectories are "chaotic" in that it may be impossible to predict which equilibria solutions are circling at a given time, t. The Lorenz Attractor is a complex region in phase space, which the trajectories shown in this simulation tend towards as t approaches infinity, which makes the rotation at the end of this animation helpful in "viewing" the chaotic attractor.

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