The space of legal configurations of the [Towers of Hanoi][1] puzzle with $n$ disks approximates Sierpinski's triangle. 

There is a Hamiltonian path in the space of configurations which can be describes as forbidding both the transition $a\to b$ and undoing the previous step. This sweeps out the approximation to Sierpinski's triangle in the same way as the L-system (reflected from the one you show). As you do this for a puzzle with $n$ disks, you can ignore the smallest disk to get a similarly restricted path in the configurations of a puzzle with $n-1$ disks.

![alt text][2]


  [1]: http://en.wikipedia.org/wiki/Tower_of_Hanoi
  [2]: https://upload.wikimedia.org/wikipedia/commons/thumb/d/da/Tower_of_Hanoi-3_Longest_Path.svg/500px-Tower_of_Hanoi-3_Longest_Path.svg.png