Lorenz System Vanessa Salas a slide with the title, your name, and a large, descriptive still image. Lorenz System Vanessa Salas

LORENZ Attractor The Lorenz system is a ODE – Ordinary differential equation first studied by Edward Lorenz. Which describes the motion of a fluid between two layers at different temperature. Specifically, the fluid is heated uniformly from below and cooled uniformly from above. While the Lorenz attractor is a set of solution that looks pretty chaotic it is a DETERMINISTIC system and not solutions are chaotic. Sensitive to the initial conditions, two initial states no matter how close will diverge, usually sooner rather than later. 1. 3 differential equations: dx/dt = σ * (y-x) dy/dt = x * (⍴-z) - y dz/dt = x * y – b * z 2. Set starting pts & take Lorenz derivative over time t 3. Set up arrays for the lines and pts & set up axis 4. Plot the background for each frame. 5. Animate it, 2 time steps per frame means that trajectories cannot cross or merge, hence the two surfaces of the strange attractor can only appearto merge. A fractal is a set of points with zero volume but infinite surface area https://en.wikipedia.org/wiki/Lorenz_system http://dis.unal.edu.co/~gjhernandezp/sim/lectures/DeterministicModelsAndChaos/lorenz.pdf

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