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A Self-reproducing Analogue

Lionel Sharples Penrose, Roger Penrose
Nature 4571, p.1183
ISSN 0028-0836
June 1957

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The most striking peculiarity of living organisms is their property of self-reproduction. The most is their property of self-reproduction. The most elementary forms, virus or phage particles, can reproduce themselves in favorable circumstances only, and this principle applies also to the multiplication of nucleic acid complexes in chromosomes. It is sometimes thought that the self-reproducing properties of nucleic acid depend upon its highly complex structure. Consequently, any mechanical analogue for self-reproduction would involve very intricate mechanisms. This does not seem to be so, and the device described here has the critical reproductive property although it is the simplest character.

A flat material, such as plywood or vulcanite, is cut into pieces with shapes corresponding to A or B drawn to scale in Fig. 1. These objects are placed on a track where they can slide freely though they cannot pass one another. The track, formed by a shelf or groove, is blocked at both ends and restricted by a roof. Horizontal shaking will cause the pieces to move both on account of their own inertia and friction and on account of collisions with one another and with the ends of the track. The pieces will not link up in these circumstances.

Two pieces, A and B, hooked together as shown in Fig. 2, are now added to those originally on the track, and shaking is resumed. The result is to reproduce the same AB complex at any point on the track whre an A-piece happens to be immediately on the left of a B-piece. If the experiment is repeated, with the alteration that the new pieces inserted are hooked together as B and A in Fig. 3, the results will be to reproduce this figure BA, at all possible places along the track.

Thus, if the pieces are arranged as in Table 1, addition of AB produces four new AB groups and addition of BA produces three new BA groups. The difference between AB and BA is analagous to a mutation in that the changed complex is repeated in its changed form. To emphasize the analogy, asymmetrical markings are shown on the surfaces of the pieces. The forms chosen here are not the only ones suitable for this type of demonstration. They need not be symmetrical, though this is useful as it increases stability in the neutral position (Fig. 1).

The example given here shows how reproduction can be demonstrated by an exceedingly simple mechanism. It has been the starting point for construction of more complicated models with similar basic properties.

Fig. 1. Elements A and B in neutral positions on the track

Fig. 1. Elements A and B in neutral positions on the track

Fig. 2. Elements A and B hooked together

Fig. 2. Elements A and B hooked together

Fig. 3. Alternative complex of B and A

Fig. 3. Alternative complex of B and A.

Table 1

(i)Original neutral arrangement.A.B.B.A.B.A.A.A.B.A.B.B.
(ii)Result after adding the complex AB.AB...AB.B.AB.A.A.A.B.A.B.B.
(iii)Result after adding the complex BA.BA...A.B.BA.BA.A.A.BA.B.B.

L. S. Penrose
University College
London, W.S.I

R. Penrose
Bedford College
Reagents Park
London, N.W.1

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