Example: LorenzAttractors
Demonstrates Lorenz attractors.
Description
This example shows the Lorenz Attractors in the different planes as well as in a three-dimensional graph. Plotted on a three-dimensional plane, a shape unlike any other forms. Instead of a simple geometric structure or even a complex curve, the structure now known as the Lorenz Attractor weaves in and out of itself. Projected on the X-Z plane, the attractor looks like a butterfly; on the Y-Z plane, it resembles an owl mask. The X-Y projection is useful mainly for glimpsing the three-dimensionality of the attractor; it looks something like two paper plates, on parallel but different planes, connected by a strand of string.
As the Lorenz Attractor is plotted, a strand will be drawn from one point, and will start weaving the outline of the right butterfly wing. Then it swirls over to the left wing and draws its center. The attractor will continue weaving back and forth between the two wings, its motion seemingly random, its very action mirroring the chaos which drives the process. The term "sensitive dependence on initial conditions" was coined to describe the phenomenon that small changes in a recursive system can drastically change the results of running that system.
To begin the example, press the Plot button. The X, Y, and Z values of the last point appear in the respective box. To see the attractor charted on the graphs, press the Chart button. You can see the current coordinates by pressing the Update XYZ button. Press the Stop Charting button to stop the charting. To see a detailed description of Lorenz Attractors, press the About Lorenz Attractors button.
Controls, Properties, Methods, and Events
This example demonstrates the following controls, properties, methods, and events:
ClearData, PlotXvsY, ChartXvsY, Axes, Plots
Example Location
Samples\Apps\LorenzAttractors