Fractal Crystal

This fractal object is constructed by starting with a first generation cube and placing a half-scale cube on the center of each face. The second-generation cubes have the same orientation as the first-generation cube. Third-generation cubes again scaled by half are placed on each unoccupied face of a second-generation cube. This process is continued ad infinitum to form a "fractal crystal". The growth of the crystal occurs more rapidly along normals to the faces of the starting cube, leading to an overall envelope (convex hull) that is an octahedron, the Archimedean dual of the cube. The sculpture includes the first 6 generations of cubes. The classical fractal known as a Sierpinski triangle occurs over and over throughout the sculpture.