File Menu

New/IFS (F5)
New/Chaos Game (F6)
New/Sierpinski Triangle Game (F9)

Choose New/IFS to get the traditional view of an iterated function system given in terms of an affine transformation of the form f(x) = Ax+b, where A is a 2x2 matrix and b is a translation vector (this is the IFS mode.) The default transformation is an IFS that scales by a factor of 1/2.

Choose New/Chaos Game to design an iterated function system based on the rules of the "chaos game" (this is the Chaos Game mode.) In this view you choose the location of your fixed points, then describe the moves of a point with respect to each fixed point. These moves consist of scaling towards the fixed point, rotation with respect to the fixed point, or a horizontal or vertical reflection across a line through the fixed point.

The Sierpinski Triangle Game is based on The Chaos Game, a java applet created by Johanna Voolich and Robert Devavey at http://math.bu.edu/DYSYS/applets/chaos-game.html. You will be presented initially with the second iteration of the Sierpinski Triangle. This consists of nine subtriangles, one of which is colored red. This is the target triangle. You will also see a blue dot at one of the three corners of the large triangle. The goal of the game is to move the blue dot into the interior of the red target triangle (so not just on the boundary, but actually inside the triangle.) Other versions of the game allow for one or three rotations with the Sierpinski Triangle iterated functions. See the individual help file for the game (also available from the Help menu when the game is started).

Open IFS File/Open Chaos Game File (Ctrl-O)
Append IFS File/Append Chaos Game File

Choose Open to load the IFS definitions from a file. If you are in the Chaos Game mode, then the Open command will load the chaos game moves from a file. This will create a new list of fractals in the Fractals menu. Choose Append to append the IFS definitions or chaos game moves in a file to the current list of fractals.

IFS files are text files using the same format as for the program Fractint. Each IFS is described using the following syntax: 

Heighway {; Heighway Dragon                                                     
; Edgar, "Measure, Topology, and Fractal Geometry"                    
; Page 19                                                            
   0.5 -0.5  0.5  0.5  0  0  0.5 
  -0.5 -0.5  0.5 -0.5  1  0  0.5 
}
The first line contains the name of the fractal followed by an opening bracket {. Anything after a semi-colon is treated as a comment and ignored (although comments can be displayed from within IFS Exploration.) There can be up to 20 lines of comments, each of length less than 70 characters.

Following the comments (if any) are lines representing each function in the IFS. There should be 6 or 7 numbers on each line. The first four are the entries of the matrix A. The next two are the entries of the translation vector. If there is a 7th number on the line, it will represent a probability. The numbers in each line should be separated by spaces, tabs, or commas. There can be at most 64 functions in each IFS.

A closing bracket } on its own line will indicate the end of the IFS definition.

A file should contain at most 30 different iterated function systems.

Chaos game files are text files that have the extension ".chg". Here is an example of a file with the code the chaos game moves for the Sierpinski Triangle. 
Sierpinski Triangle { "Chaos Rules"
;Math Horizons, Nov. 2004
;Bob Devaney
  S  0.500000  0.000000  0.333333  0.000000  0.000000 
  S  0.500000  0.000000  0.333333  1.000000  0.000000 
  S  0.500000  0.000000  0.333333  0.500000  0.866025 
}

The first line contains the name of the fractal followed by an opening bracket {. Following the comments (if any) are lines representing the chaos game moves. There should be 6 items on each line. The first is a string containg the four possible moves (S-scaling, R-rotation, H-horizontal reflection, and V-vertical reflection). Following this are the scaling factor, the rotation angle, the probability, and the coordinates of the fixed point. The numbers in each line should be separated by spaces, tabs, or commas.

Save IFS Fractals List/Save Chaos Game Fractals List
Save IFS Fractals List As/Same Chaos Game Fractals List As
Save Current IFS to File/Save Current Chaos Game to File

The first two items will save the list of iterated function systems in the Fractals menu to a text file. The last item will save only the current IFS to a file. If you are in the Chaos Game mode, only the chaos game moves will be saved to the file.

Save Fractal Picture
Save Design Picture

These items will save either the picture in the Fractal window or the picture in the Design window to a file in the form of a bitmap. The program does not support saving images as GIF or JPEG files. You can open the bitmap image in a graphics program that is capable of saving images in other formats. Alternatively, you might want to try the free program Giffy 2.3 that can convert BMP files to GIF format. The author of this program no longer supports it, however, and the website is no longer active. Since the licence says that the "program is FREE to distribute on any kind of media," I have made it available from the same website as IFS Construction Kit.

Note: You can get Giffy to automatically convert images via a right click with the mouse by running the setup program. However, I had to edit the registered file type setting via folder options to enclose the program path in quote marks. Choose the "File Types" tab, then choose the BMP extension and click on "Advanced". Choose "GIFFY, Convert to GIF" and click on "Edit...". In the textbox for "Application used to perform action", put quotes around the path to giffy.exe. Now you can select a BMP file, or select multiple files, by clicking with the right mouse button and choose "GIFFY, convert to gif".

Save Initial Polygon

This will save the initial polygon used in the Design window to a text file as a list of coordinates.

Print

The Print dialog box allows you to print the images in the fractal and design windows, the IFS code in matrix and scale/rotation form, and the chaos game rules. There are several options available for adjusting the layout of the printed items.

While you can choose which printer to use, you will not have access to a separate dialog box that handles the preferences for that printer. In addition, there is no way to change the format of the text. If you need more control over the format, you can print the IFS code to a text file which you can then open in Notepad, Wordpad, or Microsoft Word. You can copy and paste the images in the fractal and design windows into Word if necessary.