The butterfly-like Lorenz attractor is a simplified model of two-dimensional convective fluid flow and is one of the best known images of chaos. Embedded in this attractor are unstable periodic orbits described by Viswanath and this model computes a number of these orbits.  Each periodic orbit is classified by the number of times the trajectory orbits the A and B fixed points before it repeats.  Note that because the attractor is chaotic and because of numerical errors and the finite precision of the initial conditions, errors accumulate and the trajectory leaves the vicinity of a periodic orbit after a half dozen cycles.

The Lorenz Attractor Periodic Orbits Model was created using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_chaos_LorenzAttractor.jar file will run the program if Java is installed.

Please note that this resource requires at least version 1.5 of Java.