Please read Notes and Credits before clicking the green flag.
This project is one in a series of projects designed to build understanding of the concept of a strange attractor. Dr. Edward Lorenz was a meteorologist and mathematician at the Massachusetts Institute of Technology (MIT). In 1963 he published a paper, Deterministic Non-periodic Flow, that sparked the study of 'chaos'. The paper can be downloaded free by clicking the following link: http://eaps4.mit.edu/research/Lorenz/Deterministic_63.pdf The continually changing "weather system" Dr. Lorenz describes in his paper existed inside a computer that, by today's standards, wasn’t very powerful. But it was powerful enough. Because convection currents in the atmosphere and oceans drive the weather, he reduced his original set of 12 "weather" equations to three equations that model convection in a fluid. Consider a box containing a fluid that contains no large scale motions. Adding heat to the bottom of the box starts a convection current that cycles through the fluid. The "weather" in the box is a function of the convection roll. Lorenz described this convection system with a set of three differential equations. Note that the variables x, y, and z change with time. dx/dt = 10y – 10x , [x = speed of convection of roll] dy/dt = -xz + 28x – y, [y = temperature gradient] dz/dt = xy – 8z/3, [z = temperature] Professor Lorenz watched the behavior of the 'weather' system by plotting the values of x,y, and z as a function of time. When these three equations are programmed and iterated, the screen will display the graceful swirls that form the Lorenz attractor. The curve never intersects itself. This means the same set of x, y, z, values never repeat. In other words, the same exact weather condition can never repeat. Due to 'sensitivity to initial conditions', long-range weather prediction is impossible. Note that the equations are differential equations like those in the Rossler Attractor. The Lorenz Attractor is a continuous-time dynamical system. To see this… Click on the green flag but do not shift into turbo just yet. ********************************************************************* Note that the points do not hop from one part of the attractor to another but follow one after the other. One can imagine a continuous line between the plotted points. This behavior is characteristic of continuous-time dynamical systems. Now shift to turbo to see the attractor. Can you identify other continuous-time attractors in this Studio?
