To illustrate this, consider the figure below. We have a point ("center") and a circle C that we wish to rotate and dilate about the center point. Assume that we have already set C as a center (choose "Center" from the "Mark" menu) and that we have already defined a custom rotation of 30 degrees and a custom dilation of 2/3. Then, when we select C the rotate and dilate buttons will become active and if we hit the rotate button followed by the dilate button, we will get the figure shown.
Perhaps we want a single transformation that does both the rotation and dilation at one time, without the construction of the intermediate circle. To define such a compound transformation, we choose "Compound..." under the "Custom" menu. A dialog box like that shown will pop up. In the upper half of this dialog box there are two lists. The list on the left, labeled ``Currently Transforms:'' contains all of the transformations that have been carried out so far, in our case the rotation and dilation. The list on the right, labeled ``Compound Transforms:'' will contain the transforms that we wish to sequence into a new compound transformation. To define this new transformation we click on the transforms in the left list that we wish to be included.
Now, let's go back to the Canvas and click on the small dilated circle. Under the "Custom" menu we now see our new compound transformation "spiral". Choose this menu item. The circle will automatically be rotated AND dilated as shown.
Deterministic
vs Random Transformations:
The three checkboxes in the middle of the Compund
Transform dialog box, the ones labeled "Deterministic Transform",
"Random Transform", and "IFS Replacement Transform" are used to create
special types of compound transforms.
Deterministic:
If we check the box labeled "Deterministic
Transform" when creating a compound transform, the component transforms
will be carried out in sequence. This is the default setting for the
dialog box. See the example above for details.
Random: If
we check the box labeled "Random Transform"
when creating a compound transform, the component transforms of the
compound transform will be randomly applied. For example, in the
example above, suppose we selected the rotation and dilation, but
checked the "Random Transform" box. When we click "Okay" another
dialog box will pop up asking us what probabilities of occurrence we
should set with each transform.
Here we have set each component transform to take place with a probability of 0.5. The two checkboxes in this dialog, labeled "Fixed update:" and "Random Update:" can be used to define two types of action for the new transformation. In the first case, one of the compenent transforms will be chosen at random, and will be thereafter fixed. In the second case, each time the screen refreshes one of the component transformations will be used to create a new object. In this example, we'll stay with the default choice - "Fixed update:"
Now, suppose we take a circle and apply this new randomized transformation. Each time we apply it, we get a rotated or dilated circle, with probaility 0.5. Here are some iterates of this process. We started with circle C'.