How to Create Fractal Transformation Movie

You can construct a sequence of movie frames that evolve from the fractal for an initial IFS (first frame) to the fractal for a final IFS (last frame). The transformation from one fractal to the other is done either by a linear interpolation between the corresponding affine maps in each IFS, or between the scaling and rotation values corresponding to the affine maps in each IFS. If needed you can swap the positions of two maps in an IFS using "Swap Transformations" in the Design menu. If the same IFS is chosen for both the initial and final frames, then the transformation is obtained by selecting one of the maps in that IFS and rotating that map through 360 degrees while keeping the other maps unchanged.

Choose New/Fractal Movie (or press F11)
Choose an initial IFS and a final IFS. The initial IFS will correspond to frame 1 and the final IFS will be the last frame of the music.
The number of transitions from the first frame to the last frame is initially set to 50. The total number of frames will be one more than the number of transitions. Decreasing the number of transitions will make the movie shorter while increasing the number will make for smoother transitions.
The number of iterations per frame is set to 10,000 by default. Increasing this number will produce a better picture in each frame, but will make the movie run more slowly.
There are several possible options from the Options menu:
- "Average the matrices" uses a linear interpolation of the affine maps from the initial IFS and the final IFS. These are the number displayed in the Matrix Function form in the IFS window. So the new IFS comes from (1-t)*f_I + t*f_F where f_I and f_F are functions in the initial and final IFS respectively, and t goes from 0 to 1 in increments determined by the number of transitions.
- "Average the Scalings/Rotations" uses a linear interpolation of the scaling and rotation factors for the functions in the initial IFS and then final IFS. These are the numbers displayed in the Scaling/Rotation form in the IFS window.
- "Treat all angles positive" converts all rotation angles to positive values before doing the interpolation when "Average the Scalings/Rotations" is chosen.
- Choose counterclockwise or clockwise to control the rotation direction when the same IFS is chosen for the initial and final IFS.
- If you select "Cycle back to the beginning", the sequence of frames will go from the first frame (initial IFS) to the last frame (final IFS), repeat that last frame an then proceed back to the first frame (initial IFS), repeating the interpolations or rotations while reversing the steps. This will therefore create twice as many frames.
- "Show Axes" (ctrl-A) will display the axes in each frame
- "Show Designs" (ctrl-D) will display a window with the IFS design for the current frame. This is based on the current initial polygon. If this window is displayed, the "Show Axes" option will also show the axes in this window. When the design window is visible, a small green square will appear in either the fractal movie window or the design window to indicate which one is active. The zoom/shift commands in the View menu (and corresponding keyboard shortcuts) apply to the active window. Click in each window with the mouse to make it active.
If you choose the same IFS for the initial and final frames, then the interpolation is based on choosing one of the functions in that IFS and rotating the design for that function through 360 degrees in increments based on the number of transitions chosen, either counterclockwise or clockwise depending on the selection in the Options menu.
The VCR like buttons are used to control the playing of the movie

Play Backwards (ctrl-P)
Pause (S)
Play (P)
Backwards 1 Frame (B)
Forward 1 Frame (F)
The View menu allows you to choose the size of the frames. There are three standard sizes of small, medium, and large (depending on the resolution of your monitor), or you can choose you own size. Smaller sizes will display a better picture for the same iterations/frame value. The restore menu item will reset the movie back to frame 1.
"Edit/Refresh Lists" is needed if you open a new IFS file while the Fractal Movie window is displayed.
"File/Save Current Frame IFS" will save the functions for the IFS whose fractal is being displayed in the current frame to the IFS Window.
You can save an individual frame of the movie as a gif, png, or bitmap image, or you can save all the frames. In the latter case, you choose a name for the image files and the program will append the frame number as it saves each frame. If you check "cycle back to the beginning", the screen display will show the frame numbers increase from 1 up to the last frame and then decrease back to 1. The individual frames saved to disk, however, will still be numbered consecutively so that each image file has a distinct number.
You can also choose to save the movie as an animated gif. You have the option of specifying the size of the frames (in pixels) which can be different than the current screen size. You can also save an animation of the design changes. In this case the phrase "-design" will be appended to the end of the file name chosen for the fractal movie. The animated gif can be set to repeat indefinitely or to play a fixed number of times. You can specify the frame rate in milliseconds. This is how long each frame will be visible before the next frame is shown. The default 100 is 1/10th of a second.
The last option is whether or not to open the finished animated gif in the Fractal Movie Viewer (unless you terminate the creation of the movie before the last frame is reached). This viewer can play back the fractal movie (animated gif). Note that the Fractal Movie Viewer has its own controls for how often the animation is played and for the frame rate. The options that you set when saving the animated gif will apply only to the saved file (when viewed in a web browser, for example).
Important Note: Saving frames or the movie as an animated requires that the file FreeImage.dll exist either in the same folder as the IFS Construction Kit program or in the windows/system folder. FreeImage.dll is included in the zip file for IFS Construction Kit that can be downloaded from https://larryriddle.agnesscott.org/ifskit.