# Lorenz Attractor

The Lorenz attractor describes the two-dimensional flow of fluids under a particular set of assumptions. It arises from the following equations, discovered by Edward Lorenz in 1963: $$$\begin{split} \frac{\partial x}{\partial t} & = \delta(y-x),\\ \frac{\partial y}{\partial t} & = x(\rho-z)-y,\\ \frac{\partial z}{\partial t} & = xy-\beta z \end{split}$$$

where $$x$$, $$y$$, and $$z$$ make up the system state, $$t$$ is time and $$\sigma$$, $$\rho$$, and $$\beta$$ are the system parameters.

The Lorenz attractor has been the subject of a book and a plethora of research papers.

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