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English: Lorenz attractor is a fractal structure corresponding to the long-term behavior of the Lorenz Attracteur étrange de The Lorenz attractor (AKA the Lorenz butterfly) is generated by a set of differential equations which model a simple system of convective flow (i.e. motion induced. Download/Embed scientific diagram | Atractor de Lorenz. from publication: Aplicación de la teoría de los sistemas dinámicos al estudio de las embolias.

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The Lorenz system is a system of ordinary differential equations first studied by Edward Lorenz.

It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight. InEdward Lorenz developed a simplified mathematical model for atmospheric convection. The equations relate the properties of a two-dimensional fluid layer uniformly warmed from below and cooled from above.

Lorenz attractor

In particular, the equations describe the rate of change of three quantities with respect to time: The Lorenz equations also arise in simplified models for lasers[4] dynamos[5] thermosyphons[6] brushless DC motors[7] electric circuits[8] chemical reactions [9] and forward osmosis. From a technical standpoint, the Lorenz system is lorfnznon-periodic, three-dimensional and deterministic.


The Lorenz equations have been the subject of hundreds of research articles, and at least one book-length study. The system exhibits chaotic behavior for these and nearby values.

This point corresponds to no convection. This pair of equilibrium points is stable only if. At the critical value, both equilibrium points lose stability through a Hopf bifurcation. Its Hausdorff dimension is estimated to be 2. The Lorenz attractor is difficult to analyze, but the action of the differential equation on the attractor is described by a fairly simple geometric model.

mplot3d example code: — Matplotlib documentation

This problem was the first one to be resolved, by Warwick Tucker in The Lorenz equations are derived from the Oberbeck-Boussinesq approximation to the equations describing fluid circulation in a shallow layer of fluid, heated uniformly from below and cooled uniformly from above.

The fluid is assumed to circulate in two dimensions vertical and horizontal with periodic rectangular boundary conditions. The partial differential equations modeling the system’s stream function and temperature are subjected to a spectral Galerkin approximation: This reduces the model equations to a set of three coupled, nonlinear ordinary differential equations.

A detailed derivation may lorrnz found, for example, in nonlinear dynamics texts. A solution in the Lorenz attractor rendered as a metal wire to show direction and 3D structure.


From Wikipedia, the free encyclopedia. Not to be confused with Lorenz curve or Lorentz distribution. A solution in the Lorenz attractor plotted at high resolution in the x-z plane. An animation showing trajectories of multiple solutions in a Lorenz system.

Lorenz attractor – Wikimedia Commons

An animation showing the divergence of nearby solutions to the Lorenz system. A visualization of the Lorenz attractor near an intermittent cycle.

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The Lorenz Attractor in 3D

Initially, the two trajectories seem coincident only the yellow one can be seen, as it is drawn over the blue one but, after some time, the divergence is obvious. Java animation of the Lorenz attractor shows the continuous evolution. Wikimedia Commons has media related to Lorenz attractors.