Self-Replicating Mechanisms/Machines

Penrose Block Replicators

The most intriguing paper of this week was Mechanics of Self-Reproduction by British mathematician Lionel Penrose in 1957.

Using the definition that a machine is "an apparatus using or applying mechanical power and having several parts, each with a definite function and together performing a particular task," the paper defines the first successful construction of an artificial self-reproducing object. Essentially, a straight track that confines two types of solid objects (object A or B) is agitated horizontally to induce a link between two dissimilar objects, either an AB complex, or a BA complex. The image can be seen here:

In the figure above, we see that parts A and B can link to form two complexes. In the example above, the BA complex is formed. If a BA complex is formed in the track (or assembled and placed into the track), further BA complexes form. Similarly, if an AB complex is formed, further AB complexes will form.

The fascinating part is that the agitations will only form duplicates of the first complex introduced into the rack. Thus the system itself is self-replicating. It does this by "activating," or tilting, the pieces to expose the appropriate binding site. Although intriguing, the system above is limited since only two types of complexes can be replicated (AB, BA). If we use the Penrose's Five Principles, we can extend this system further.

  1. Units must each have at least two possible states.
  2. Machine must have definite boundaries.
  3. Kinetic energy must be captured and held as potential energy (ratchet, catch, hook)
  4. Transference of activation; capability of communicating its state to another unit in close contact
  5. Catalyst (in this sense, the track facilitates the process of linking)

From these principles, we can derive complexes with more states and dimensions.

So what I did was model the mechanism of a 2 block 1D penrose self-replicating machine. I used SolidWorks to create A (green) and B (red) parts and a track for them to lie in. In my assembly, I mated the pieces so they wouldn't "fall off" the track. I then moved each component using "Move Component" and selecting the "Physical Dynamics" radio button. This incorporated collision detection and allowed the walls of the track to restrict the motion of each piece.

Perfect A B pattern

This initial condition assumes an alternating patters of A and B pieces. As I move one piece left and right, I form a complex. As I move that complex further, I form duplicates of the original complex formed.

Still make A-B complexes without perfect pattern

Even if there is a piece out of order in between two complexes, the piece is activated with it's non-binding side, furthering the KE of the first complex, and still activating the appropriate piece to create a duplicate.

Perfect A B pattern

In this last example, I show that, although I was able to form an BA complex, the further propagation of the pieces did not form any replicates because there was no A to the right of a B piece.