Geometer's Sketchpad  
Fractal Tree

Construction

Setting Up

  1. Open up a new sketch.

  2. Choose new script from the File menu. Click on the script's Record button.

  3. In the new sketch set up points A, B, and C, connected by segments num and den as shown below. Next, place two more points (root and fork).

  4. Select segments num and den. Choose Mark Ratio from the Transform menu. This ratio will define how much the branches of the tree shrink or grow from one generation to the next.

Scripting One Generation

  1. Construct a segment from point root to to point fork.

  2. Select point fork and choose Mark Center from the Transform menu.

  3. Select point root and choose Dilate from the Transform menu. Make sure "By Marked Ratio" is chosen before clicking on OK. This should give you point root'.

  4. Rotate root' by 180° about fork resulting in point root''.

  5. Mark angle ABC (using the Mark Angle command in the Transform menu) and rotate point root''. Then mark angle CBA and rotate point root'' again. This should give you two images, each rotated in the opposite direction.

  6. Connect with point fork with each of the root'' images. Your sketch should look like the one shown below.

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