Draw Menu
Random (F7)
Deterministic (F8)
The item that is checked will determine which of the two algorithms are used for drawing the fractal. The deterministic algorithm is also called the Multiple Reduction Copy Machine (MRCM) algorithm in some books.
Draw (Ctrl-D)
If the random algorithm is used, choosing Draw will plot iterations until the "Q" button is pressed or some other window gets the focus. If the deterministic algorithm is used, choosing Draw will draw the next iteration of the IFS.
Scale to Fit (Ctrl-W)
Scale to Design Window (Ctrl-G)
Choose Scale to Fit to set the scale so that the entire fractal will be visible in the window. Choose Scale to Design Window to make the scale of the Fractal window identical to the scale of the Design window.
Freeze Scale
Selecting this option will freeze the scale used in the fractal window so that no changes can be made. This is useful if you want to draw different fractals using the same scale for each (for example, if preparing an animation.) Scale to Fit, Scale to Design Window, and the various zoom and shift options will be disabled until Freeze Scale is unchecked.
Shift (arrow keys)
You can shift the viewing window left, right, up, or down in increments of 1% using the menu or the arrow keys. Any image in the window will appear to shift in the opposite direction.
Zoom In (Selection) (Page Up)
Zoom Out
The fractal window will zoom in by 5%. You
can also zoom in on part of the fractal by using the mouse to draw a selection rectangle. The menu will change from Zoom In to Zoom Selection. Hold down the shift key to make the selection rectangle a square (and preserve equal scale on both axes.) This item is only available when using the random algorithm. You must stop drawing before you can zoom, but if a fractal has already been drawn, the program will redraw it after the zoom.
Choose Zoom Out to zoom out 105% (Page Down), 125%, 150%, or 200%. You must stop drawing before you can zoom, but if a fractal has already been drawn, the program will redraw it after the zoom.
Restore (Home)
Restores the viewing window to the original dimensions obtained from scale to fit.
Clear (Delete)
Clears the Fractal window without changing the scale.
Add Picture (Initial Set)
When using the deterministic algorithm, you need to add a picture to the Fractal window to be used as the initial set for the iteration of the IFS. There are seven choices. You can use the current design polygon (as an outline or filled), a triangle (equilateral or right), a rectangle, a regular polygon (up to nine sides), a circle, or an image loaded from a bitmap, GIF, or JPEG file. You can also paste an image from the clipboard. Choosing the filled design polygon brings up a dialog box in which you can choose the fill color. The boundary can be either visible (black) or invisible. Choosing a rectangle, triangle, reglar polygon, or circle will bring up a dialog box in which you can choose the size, the style (outline or filled), and the color. Click on the color box to choose a different color. When you first load an image from a file or paste an image from the clipboard, you may move the image to a desired location using the mouse as long as the image is surrounded by a dotted outline. Once the image is in the appropriate place, click anywhere outside the image to make the position permament.
Colors
This option is only available when using the deterministic algorithm. Choose Use IFS Colors to draw each point based on the color of the function used from the IFS. Choose Use Image Colors to draw each iterated point based on the color of the original point in the image. If you add a picture to the Fractal window from a file, Use Image Colors will be the default choice for the color scheme.
Overlay Images
This option is only available when using the deterministic algorithm. It will draw the result of each new iteration on top of the images obtained from earlier iterations.
Trace (Ctrl-T)
This option is only available when using the random algorithm. If Turn Trace On is checked, then a ctrl-right click with the mouse will plot a point in the Fractal window that will serve as the initial seed for tracing an orbit. You can also choose Set Initial Point to enter the x and y coordinates of the initial seed. Press the space bar to randomly pick one of the functions in the IFS which is then applied to the last point plotted. Instead of allowing the functions of the IFS to be
chosen randomly, you can specify exactly which function will be executed in the next step of the orbit by pressing the corresponding number. Hold down the ctrl key for numbers greater than 10 (i.e. ctrl-1 = 11, ctrl-2 = 12, ..., ctrl-9 = 19, ctrl-0 = 20.)
Choose Color Dots or Black Dots to specify how the points in the orbit will be colored. Colored Dots will use the color of the corresponding function from the IFS window.
If you hold down the left mouse button when the cursor is over the tracing message box in the lower right corner, a window will popup summarizing the instructions for how to trace.
Fixed Points (Ctrl-F)
Checking Show Fixed Points will plot the fixed points for the functions in the IFS. Choose Color Dots or Black Dots to specify how the fixed points will be colored. Color Dots will use the color of the corresponding function from the IFS window.
Show Axes (Ctrl-A)
If checked, will show the axes in the Fractal window.
Show Grid (Ctrl-G)
If checked, will draw a grid in the Fractal window. The default grid size is 0.1. Use the plus and minus keys to rotate among four grid sizes (0.05, 0.1, 0.125, and 0.25).
Set Background Color
Opens a dialog box that can be used to pick the background color for the fractal window. Changing this color might require you to also change the axis color to make the axes visible.
Set Axis Color
Opens a dialog box that can be used to pick the color for the two axes.
Tiling Options
Allows you to try to tile the plane with the current fractal. You must specify the two vectors that describe the directions in which the tiling is done. If these vectors are v and w, then copies of the fractal are made in the direction nv+kw for integer n,k from -R to +R, where R is the tiling radius. If the tiling radius is 0, only the original fractal is drawn.
If the IFS is obtained from a design using an integer matrix, the initial values for v and w will be the vectors from that matrix. These may need to be adjusted based on the choice of residue vectors.
It is sometimes helpful to measure distances in the Fractal window to know how to choose the vectors v and w. This can be done by pressing the left mouse button while holding down the ctrl key. Continue to press the button and move the cursor to another location. The message box in the lower left corner will display the change in x and the change in y between the two points. The line connecting the two points and the Δx and Δy values will disappear when you release the mouse button.
The tiles can be colored using the same colors as for the IFS, or each copy of the fractal can be colored in a solid color.
Fractal Image Size
Choose "Set Image Size" to set a specific size (width/height) for the image pane in which the fractal image is drawn. This can be given in terms of pixels, inches, or centimeters. The size is restricted to 12 inches by 12 inches. If the image size is too large to fit inside the fractal window, scroll bars will be added. Thus for large image sizes, this option is primarily of use if you want to save the fractal image to a bmp file or copy it for pasting into an illustration program (e.g. Paint Shop Pro or Photoshop).
Image window is 600x600 pixels, so scroll bars added
Selecting "Unfreeze Image Size" will reset the image pane so that it will fit inside the fractal window.