Sierpinski Tetrahedron

The Sierpinski Tetrahedron is a 3D fractal in the Mathematical world. It is defined recursively, where each level is constructed from components of the previous level. Like its cousin the Menger Sponge, one can create a complex structure by applying a few simple rules over and over.

Actually, you don't need a plugin to do this. You can create any level of the Sierpinski Tetrahedron just using the SketchUp GUI. This plugin was basically an exercise in using the SketchUp Ruby API to build complex components from subcomponents. I left the source code unscrambled, if anyone wants to see how it works.

To construct the first level, start with a simple tetrahedron, scale it down to one-half size, make four copies, and arrange them in the tetrahedron-like shape pictured to the right. This is the first level tetrahedron.

To construct the second level, apply the same procedure to the first level tetrahedron. The result is the second level tetrahedron.

For any level, apply the same process to four copies of the previous level tetrahedron. This plugin will construct the Sierpinski Tetrahedron up to the seventh level.

This plugin is accessed from the Draw menu (Draw > Sierpinski Tetrahedron). This will open a dialog box to enter the parameter values.

The outside color was left undefined, and shows up as white by default. You can easily change the outside color by clicking anywhere on the component with the paint bucket.

You can change the color of the inside faces almost as easily. Open the component by double-clicking on it with the select tool. The faces are grouped by material. So, if you click on any inside face with the paint bucket, all the faces that are the same color will be painted.

When you click OK, the Sierpinski Tetrahedron is created as a component, and the component placement tool is activated to position it in the model.

The dialog box remembers the values between SketchUp sessions.