Random Iterated Points

Sometimes you may find yourself specifying a point on an object as the first image of an iterated pre-image. For instance, rather than map a triangle’s vertices to its midpoints as in the other examples, you might map a triangle’s vertices to arbitrary points constructed on its three segment edges. In this case, the Structure pop-up menu gives you the choice of how you want Sketchpad to iterate these arbitrary points on objects. When you choose To Same Relative Location, Sketchpad displays each iterated image point at the same relative location as that first image you chose in the Iterate dialog box. If you drag that first image point to a new position on the path on which it’s constructed, all of the iterated images adjust to the same relative new position. On the other hand, if you choose To New Random Locations, each iterated image of your initial point appears at a new, random location on its (iterated) path, independent of the location of the first image. This choice is useful if you’re exploring geometric probability or other applications of randomness.

After you’ve constructed an iteration, you can use its Iteration Properties to experiment with both choices for how to iterate points constructed on path objects.