dx/dt = S (y - x)where the parameters of the problem are S = 10, B = 8/3, and R is set by the user. The system can undergo periodic or chaotic behavior, as well as converge to a fixed point; the behavior is determined by R. The characteristic butterfly shape of this "strange" attractor is well known.
dy/dt = (R - z) x - y
dz/dt = x y - B z
The numerical integration employs an adaptive step size, and the initial conditions are fixed. The solution (a curve in three-dimensional space) is shown in plane projection, with adjustable orientation and position. The most recent 20,000 (or less) solution points are displayed at any time. The color changes gradually as the computation proceeds.
Available user controls are the start/stop and reset buttons, and a pair of sliders for coarse and fine adjustment of the "R" parameter. Dragging with the mouse (left button pressed) changes the orientation; shift+drag moves the display in the image plane and control+drag zooms the image.