1 Introduction
The applet is divided into two halves. The left half allows the user to obtain a time series. The right half displays the attractor corresponding to the time series in the left half of the applet.

2 Obtaining a time series
The user can either generate a time series chosen from the menu, or read a time series from a data file.

2.1 Generating a time series:

Step 1: There are 9 pre-set choices in the menu, representing 4 systems of equations: Logistic, Henon, Lorenz and Rossler. The Henon map has two choices because a time series can be generated by the x- or y-coordinate respectively. The Lorenz and Rossler system each has three choices, corresponding to the x-, y-, and z-coordinate respectively. The 10th choice in the menu is read from file.

Step 2: After a choice is made from the menu, irrelevant input areas will be disabled. The user can change the parameters in the active input areas. Parameters a,b,c are the constants used in the equations. Initial x,y,z are the initial values of the x-,y- and z-coordinate. Increment ODE is the step size used in solving the Lorenz or Rossler differential equations. Sampling is the time increment between successive sampling points to be included in the time series, and it must be an integral multiple of ODE. The applet will automatically correct the value in Sampling if it is not an integral multiple of ODE.

Step 3: The user can specify the length of the time series. Maximum length is pre-set to 500000.

Step 4: Clicking the Generate button will generate and display the time series. The user can adjust the scroll bar to view various portions of the time series.

2.2 Reading a time series from file:

Step 1: The data file must be a text file. Lines starting with the symbol # are reserved for comments and will be ignored by the applet. Each line of the data file may contain any amount of numbers seperated by a space in between.

Step 2: If the data file is residing in the same directory as the applet, the user can type in the file name in the Read file input area. If the data file is in a subdirectory, the user can use the format "[subdirectory]/[filename]". Otherwise, the user can type in the complete URL of the file, eg. http://... or file://...
(Note: If the applet is run from a remote server, the user may not be able to read a file from the local computer; therefore, it is advised that the user download the applet to the local computer before running.)

Step 3: Click Read to read in the data file.
 

3 Reconstructing Attractor

3.1 The user can specify the parameters used in the reconstruction:
            (i) Time lag is an integer representing the number of sampling points skipped between 2 coordinates.
            (ii) 2-D or 3-D is the dimension of the reconstruction.
            (iii) Ignore Beginning specifies how many numbers in the beginning of the time series to be ignored.
            (iv) End allows the user to trim the time series at the end.

3.2 Clicking Reconstruct will reconstruct and display the attractor using the time series in the left half of the applet.

3.3 The user can zoom in or out by clicking + or - respectively; re-center the image by clicking on a point. If the attractor is in 3D, the user can drag on the image to rotate. Clicking reset will reset the transformation to the original position.

3.4 Checking the box Coordinate.axis will display the coordinate axes in green when the image is redrawn. Checking the box rotate.axis will display the rotational axes in yellow. Checking the box preview will display the entire image during rotation; otherwise, the image will only be displayed after the user release the mouse button from dragging.

3.5 If the times series used is Lorenz or Rossler, clicking Reference will display the attractor based on the (x,y,z) coordinates instead of reconstructing the attractor from a time series.

3.6 The fractal dimension will be calculated and displayed. The algorithm used is based on codes provided by the course instruction, Dr. Randall Pyke. The image is divided into 100-square grids on each side. Then box-counting is done using square size of  2,5 and 10 squares respectively.

4 Size of the Applet
The applet must be run with a size of at least 640-pixel in width and 400-pixel in height.