Multiple Iteration Maps

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Multiple Iteration Maps

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

For some 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 binary tree splits in two at each junction, so the iteration rule has two maps: one to produce the right branch (Map #1) and one to produce the left branch (Map #2).

Similarly, a parallelogram tessellation requires you to iterate the original parallelogram both horizontally (Map #1) and vertically (Map #2).

To create such an iteration, select the seed points and choose Transform | Iterate. In the Iterate dialog box, define the first map normally. Then choose Add New Map from the Structure pop-up menu and define the second map. After you define all the maps that make up your iteration rule, click Iterate.

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

See How to Construct a Sierpiński Gasket for step-by-step directions to create a famous fractal.