We first study the time variation of X(t), Y(t), Z(t) i.e. the evolution of the point in phase space representing the state of the system. The phase space is three dimensional, but it is easier to study projections onto the various coordinate planes - here the X-Z plane.
Read the instructions on how to use the applet. You will usually want to increase the iteration speed using the slider (but increasing it too far may crash poorer Java implementations).
The plot shows the famous Lorenz butterfly. The plot appears to contradict one of the ideas introduced in the introduction: which one and what is the resolution?