Using the Iterate Dialog Box

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Using the Iterate Dialog Box

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When you choose Transform | Iterate, the Iterate dialog box appears.

Drag the Iterate dialog box out of the way if it’s hiding the destination images you want to click.

Use the top part of the dialog box to specify the mapping used at each step to create the next iteration image. Fill in each box of the right-hand column by clicking in the sketch on the object to which each pre-image object should be mapped.


To make this easier, Sketchpad highlights in the sketch the pre-image object currently being matched. For instance, in this example, Sketchpad highlights point A in the sketch when it’s time to click the object that point A maps to. Sketchpad then highlights point B in the sketch when it’s time to click the object that B maps to, and so forth.

Use the Display Pop-up Menu to Control the Appearance of the Iteration.

Increase or Decrease Iterations: Increase or decrease the number of times your rule is iterated. You can also use the + or keys, without opening the Display pop-up menu, to increase or decrease the number of iterations.

When you’re creating an iteration using parametric depth, you cannot change the number of iterations by hand.

Display the Full Orbit or Final Iteration Only: Display all iterations, or only the final iteration. When you display all iterations, the set of all images of an iterated object is sometimes called the orbit of that object.

It’s often convenient to display all iterations when you’re iterating using a single map, and to display only the final iteration when you’re iterating using multiple iteration maps.

The Transform | Terminal Point command allows you to construct a final iterated point image as an actual point that you can use in further constructions.

Use the Structure Pop-up Menu to Control the Structure of the Iteration.

Add/Remove Map: Add a new iteration map or remove the current map.

Create Images: Create images of all objects that depend on the selections or create images of only the nonpoint objects.


Often — especially when working with multiple maps — you won’t want to see the iterated images of points, but only of segments, polygons, and so forth. Sketchpad automatically switches this option — to only create nonpoint object images — when you start working with multiple maps, though you can switch it back if you prefer to create point images as well as nonpoint images.

Tabulate Values: Determine whether to create a table of all iterated measurements.

Move Points on Objects: Set iterated points on objects to stay at the same relative location as the original or set them to use new random locations each time they’re iterated.

Finalize the Iteration

Once you’ve specified the destination for each selected pre-image, click Iterate to finalize the iteration.

The constructed iteration appears. Use Iteration Properties to change the depth or other characteristics of the iteration.

You can see step-by-step examples of using this dialog box to create a geometric iteration, a numeric iteration, and a   Sierpiński gasket(using multiple iteration maps).