LiveGraphics3D Example:
The Sierpinski Tetrahedron

First Step

This example was created with the help of some Mathematica code written by Robert M. Dickau available on his homepage.

The Sierpinski tetrahedron is the three-dimensional version of the famous Sierpinski gasket. (To imagine it just think of all tetrahedrons being replaced by triangles.) The Sierpinski gasket is in fact shown in almost any book about fractals. See Stan Wagon's book "Mathematica in Action" for a construction with Mathematica.

Second Step

This graphic was constructed by replacing each of the tetrahedra of the first step by four smaller tetrahedra.

Third Step

This object consists already of 256 triangles which is more than enough considering the size of its description and the performance needed to rotate it in real-time.

Martin Kraus, April 15, 2021