Plots the time evolution of the variables X,Y,Z.
The full dynamics needs to show the three variables
as they vary in time. On the computer screen it is easiest to show
various *projections* such as the *Z-X* projection.
The two variables plotted are chosen by the *x-ax* and
*y-ax* parameters with *1* standing for *X*, *2*
for *Y* and *3* for *Z*.

To study the sensitivity to small changes in initial conditions, set
*dX0, dY0, or dZ0* to a small value. Two traces will be seen, corresponding
to the two orbits starting from the initial points *(X0,Y0,Z0)* and
*(X0+dX0,Y0+dY0,Z0+dZ0)*.

Plots the power spectrum of the variable defined by *y-ax*. The power spectrum is generated
by successively accumulating *Points* number of points spaced by *Interval*
time steps *dt*, performing a fast Fourier transform on these points, and calculating the
magnitude squared to give the power spectrum of this segment of data. This is then averaged in with
the power spectrum of previous segments. The maximum frequency in the power spectrum is the Nyquist frequency
*(Interval*dt)**(Points*Interval*dt)*

Segmenting the data introduces apparent discontinuities in the data to be transformed, which
leads to broadening of the transform even for periodic signals and to high frequency tails. These
effects are reduced by multiplying each segment by a window function that goes continuously to zero
at the beginning and end of each data segment. The windowing function used is set by the parameter
*WinNum*:

WinNum | Window | Description | Singularity in: |

0 | None | Top Hat | Function |

1 | Bartlett | Tent | First derivative |

2 | Welch | Parabolic | First derivative |

3 | Hanning | Sinusoidal | Second derivative |

For more details see "*Numerical Recipes*" by W.H. Press et al.

Plots the intersection points of the orbit with a two dimensional plane. The plane
is defined by *X=const, Y=const,* or *Z=const* depending on the choice of *Variable*,
with *const* set by the parameter *Section*

Plots the return map of successive maxima of one variable (chosen by *Variable*). This type of plot
was introduced by Lorenz in his original study.

Reconstructs trajectory using time delay coordinates. A reconstructed phase space is constructed from *V(t), V(t+T), V(t+2T)*, with *V* either *X*,*Y*, or *Z* depending on the value of *Variable*, and *T* the delay time given by *Delay x dt*. The projection of this 3-dimensional space plotted remains determined by *plot_x* and *plot_y*.

[Equations] [Instructions]

Last modified Tuesday, December 30, 1997

Michael Cross