The Sierpinski arrowhead curve is a classic fractal that approximates the Sierpinski triangle. Like many two-dimensional fractal curves, it can be extended to three dimensions; this extension approximates the tetrix (or Sierpinski tetrahedron).
Snapshot 1: creation of the figure begins with a simple seed
Snapshot 2: each iteration is created by rotating and translating the previous image in such a way that the endpoints match up, making an unbroken curve; increasing the "stretch" factor between iterations emphasizes how the figure is connected
Snapshot 3: higher iterations approximate the tetrix