Iterations in Sketchpad are powerful and flexible. Here are some of the ways they can be controlled and displayed.
Set Iteration Depth Manually You can change the depth of an iteration in several ways. To begin, select one or more iterated image objects. •Press the + or – key. Each press of the key increases or decreases the depth of iteration by one. •Choose Increase Iterations or Decrease Iterations from the Context menu. •Choose Edit  Properties  Iteration and type a value for Number of iterations. No matter which method you use, the minimum depth is one, and the maximum depth is limited by the number of iteration samples that can be displayed. You can choose Edit  Advanced Preferences  Sampling to change the maximum number of iteration samples allowed. Set Iteration Depth Parametrically When you define an iteration, use a measurement, parameter, or calculation in your sketch to automatically determine the depth of the iteration. First select the points or parameters that define the preimage, and then select the value that defines the iteration depth. (The depth value must be the last object selected.) Hold the Shift key while you pull down the Transform menu, and the Iterate command changes to Iterate to Depth. Choose this command and use the Iterate dialog box to define the iteration normally. Once the iteration is defined, the integer part of the depth value determines the iteration depth.


The number of rows in a table of iterated values changes automatically as you increase or decrease the depth of iteration. If you don’t want to create the table of iterated values, uncheck Tabulate Iterated Values in the Structure popup menu of the Iterate dialog box. If you create a table when you create the iteration and decide you no longer need it, select the table and clear it from your sketch. 


Use multiple iteration maps to make each step of the iteration produce two or more copies of the original objects. Multiple maps allow you to create iterated fractals and tessellations such as the Sierpiński gasket, a binary tree, or a parallelogram tessellation. 
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