Multiple Iteration Maps

By specifying a destination point for each of the iterated independent points, you create a single iteration map. This map describes how to transform the pre-image to create a transformed copy of the original objects. For most iterations, each iteration step produces a single copy of the original objects. For such iterations, the iteration rule consists of a single map.

But for other iterations, one step of the iteration produces two or more copies of the original objects. Each such copy of the original objects requires its own map, so such iterations require multiple maps. For example, a parallelogram tessellation requires you to iterate the original parallelogram both horizontally and vertically.

Fractals and tessellations are the most common geometric constructions for which the iteration rule requires multiple iteration maps.

To construct an iteration with multiple maps, specify the first map as in steps 1–3 in "Using the Iterate Dialog Box". Then choose Add New Map from the Structure pop-up menu and specify a second map by clicking in turn on a new destination for each of the original points. When you’re finished specifying all the maps that make up your iteration rule, click Iterate.