A Novel Pathway to First-Generation Molecular Assemblers

(c) 1998 Robert A. Freitas Jr.

18 November 1998


Abstract. A new class of manufacturing systems called kinematic-diffusion assemblers possibly could be fabricated today and could in principle serve as simple first-generation submicron-scale molecular assemblers.


1. Introduction

Drexler [1] proposed the concept of mechanical assemblers capable of manipulating matter at the molecular level to create structures with atomic precision. Subsequent discussions of possible pathways towards this goal [2-4] have included rather complex designs that do not appear to be readily implementable as first-generation assemblers using existing, known, or projected techniques. This paper explores a new class of manufacturing systems, readily scalable from micron to nanometer regimes, which can in principle serve as first-generation assemblers. These devices possibly could be built today using conventional techniques. The arguments advanced are mainly qualitative; a few numbers are introduced at the end to verify general feasibility and to lend concreteness to the discussion.


2. The Fallacy of the Substrate

To generate macroscopic quantities of useful products using nanoscale manufacturing systems, huge numbers of such systems must join in the work. Building a huge number of microscopic systems one by one is time-prohibitive, hence the concept of self-replication is key to all known proposals for rapid molecular manufacturing.

As conceived by von Neumann [5] and subsequent researchers [6], the most general theoretical conception of physical replication views replication as akin to a manufacturing process. In this process, a stream of inputs enters the manufacturing device. A different stream of outputs exits the manufacturing device. When the stream of outputs is specified to be identical to the physical structure of the manufacturing device, the manufacturing device is said to be "self-replicating."

Note that in this definition, there are no restrictions of any kind placed upon the nature of the inputs. On the one hand, these inputs could consist of a 7,000 oC plasma containing equal numbers of atoms of all 92 natural elements -- by some measures, a "perfectly random" or maximally chaotic input stream. On the other hand, the input stream could consist of cubic-centimeter blocks of pure elements. Or it could consist of prerolled bars, sheets, and wires. Or it could consist of pre-formed gears, ratchets, levers and clips. Or it could consist of more highly refined components such as pre-fabricated motors, switches, gearboxes, and computer chips. A manufacturing device that accepts any of these input streams, and outputs precise physical copies of itself, is clearly self-replicating. Thus the common belief that only assembly from highly disordered substrates counts as true replication is clearly fallacious. In fact, construction of self-structure from any stream of inputs, however ordered or disordered, represents self-replication.

The 1980 NASA study on replicating systems [7] offered an amusing illustration of the Fallacy of the Substrate with its example of a self-replicating PUMA robot. This robot was conceptualized as a complete mechanical device, plus a fuse that must be inserted into the robot to make it functional. Here the input substrate consists of two distinct parts: (1) a stream of 99.99%-complete robots, arriving on one conveyor belt, and (2) a stream of fuses arriving on a second conveyor belt. The robot combines these two streams, and the result of this manufacturing process is a physical duplicate of itself. Ergo, the robot has "replicated."

In principle, different replicator designs might metabolize any of an infinite number of input substrates. Depending upon its design, a particular device may be restricted to replication from only a very limited range of input substrates. Or, a device may have sufficient generality to be able to replicate itself from a very broad range of input substrates. In some sense this generality is a measure of the device's survivability in diverse environments. But it is clearly fallacious to insist that "replication" can occur only when duplication of the original manufacturing device takes place from some ill-defined, highly-disordered substrate.


3. Replicating Systems May Be Very Simple

The theory of self-replication was first examined by von Neumann [8], who concluded that machine replication was possible and that perhaps twelve different kinds of units of unknown complexity could be required as building materials. Falling prey to the Fallacy of the Substrate, Haldane [9] inferred that as many as ~105 parts might be needed to make a replicator. This inference was refuted just three years later with the arrival of the first in a series of ingenious designs for mechanical self-replicating machines that were built and operated in the late 1950s. In the first example [10], a pair of joined ratchetlike blocks, when placed in a "sea" of left and right blocks and then physically agitated, replicates itself from this well-ordered input substrate, making more block-pairs until all the single blocks are used up, a process similar to chemical autocatalysis. More complex congeries of blocks, including clever four-block, eight-block, and 12-block replicators that could replicate in a sea of blocks were demonstrated by Penrose [11, 12]. Jacobson [13] demonstrated a 3-unit replicator consisting of toy train engines circulating on HO model railroad tracks, and Morowitz [14] designed a simple two-unit device with one unit comprised of about a dozen components including switches, batteries and electromagnets, that could assembly copies of itself from parts floating on the water surface of a bathtub. Three important conclusions may be drawn from the above examples.

First, replication is fundamentally so simple a task that machines capable of displaying this behavior pre-date most of the modern electronic computer era.

Second, assembly is an inherently simpler operation than fabrication. A complex part may embody hundreds or thousands of prior fabrication and assembly operations, yet may be installed within an assemblage in a single step. Hence assembly is an easier candidate for early implementation in first-generation self-replicating manufacturing systems than is fabrication.

Third, and most important, the simplest replicator may require assembly, but no fabrication, in order to replicate itself. A machine capable of assembly alone can replicate itself only from a very limited set of input materials, but such a machine can be extremely simple both in structure and function. However, a machine capable of assembly and fabrication can replicate itself from a more diverse and disordered set of input materials -- but only at the expense of far greater internal structural and functional complexity.


4. Manufacturing Useful Products

Given an appropriately well-ordered input substrate, the devices described in the previous Section can replicate themselves but can produce no other output structure. To be useful in manufacturing, a replicating system must not only be able to manufacture its own structure from the available input substrate, but it must also be able to manufacture useful products that differ from its own physical structure [7].

In the context of molecular nanotechnology, the simplest useful first-generation free-standing assembler will be a molecular manufacturing machine that is capable of self-replication and produces some useful product. Useful products might include linked nanoscale gear trains, nanopistons for acoustic sensing and power transduction, or various components of the mechanical nanocomputer described by Drexler [2].

Consider a class of simple assembler that assembles structures using externally-produced parts. These parts are fed to the assembler as feedstock. The assembler then assembles the parts into multi-part congeries. These congeries may themselves be treated as input substrate by successive species of assemblers to build still larger congeries, yielding increasingly complex structures in the manner of a convergent or hierarchical assembly [2, 15].

Depending upon the physical scale of the assembler, externally supplied parts may be manufactured to ~<1% precision in large numbers by currently available fabrication techniques. Such techniques may include conventional milling and drilling, microlithography and MEMS, microcontact printing, electron-beam lithography, biochemical synthesis, polymer or fullerene chemistry, self-assembly or thin-film methods, supramolecular synthesis, or some combination thereof.


5. Kinematic-Diffusion Assemblers

The designs presented here are offered in the spirit of a thought experiment and not as serious proposals intended for immediate construction. However, they represent a novel class of kinematic assemblers that should be amenable to construction using presently-available tools, and might allow construction of more complex tools that could lead to full positionally-controlled molecular assembly after a few developmental generations.

The two most fundamental assembly operations are insertion (e.g. translation of grasped parts) and twisting (e.g. rotation of grasped parts). Section 5.1 presents a schematic design for an extremely simple assembler that can insert one grasped part into another grasped part. The Insertion Assembler itself consists of only 8 parts, and may in turn be assembled using only insertion operations, hence is self-replicating. Section 5.2 presents a schematic design for an assembler that can rotate one part that has already been inserted into another part. The Rotation Assembler also has just 8 parts and may be assembled using only insertion operations. Additionally, both the Insertion Assembler and the Rotation Assembler are designed to be capable of sequential self-assembly in the absence of any working assemblers, thus avoiding the classical chicken-and-egg problem.

All assembly is performed in fluid suspension both to simplify parts transport and presentation, and also to eliminate electrostatic, van der Waals and other unwanted adhesion forces. Materials and assembly fluids can be selected to reduce the Dupre reversible work of adhesion (energy per unit area) to near zero, thus minimizing inter-part surface adhesivity effects.

For each example, we first describe the proposed assembler structure, followed by the operation of the assembler as it assembles a useful product. Insertion Assembler self-assembly sequences are described in Section 5.3; assembly of more complex products and the possibility of future-generation kinematic-diffusion assemblers are described in Section 5.4.


5.1 The Insertion Assembler

Consider as a prototypical useful product the interlock logic gate in the nanomechanical computer described by Drexler [2]. Abstracting from this product, the simplest possible assembly operation is one in which a cylindrical peg, part "P", is inserted into a housing containing a complementary lengthwise hole, part "H". (Two such operations, performed sequentially, would manufacture an interlock logic gate.) Essential assembler elements include mechanisms for parts identification, grasping and orienting both parts, bringing both parts together via mechanical translation, for releasing the completed assembly, and for resetting the device for the next cycle. Parts are brought to the device via diffusion-like processes, hence the name "kinematic-diffusion" for this class of device.

Figure 1 shows the individual parts that comprise the Insertion Assembler. In Figure 2, these parts are shown already in place in a completed assembler. In brief, there is an actuator module comprised of two parts, the P-capsule and the H-capsule, each a polygonal cylinder capped at one end. The P-capsule is slightly narrower and fits inside the H-capsule in the manner of a gelatin pill from the drugstore, except that their mouths have complementary circumferential flanges to preclude separation after the two capsules have been joined. Each capsule bears a single surface depression of triangular shape and trapezoidal subsurface aspect which incompletely penetrates the wall; the actuator interior contains a volatile working fluid.

Attached to the Actuator at each triangular surface depression is a parts receptor. There is a parts receptor for Part P, the P-receptor, and a parts receptor for Part H, the H-receptor. Each parts receptor is comprised of three elements: (1) a Screen, consisting of a flat plate penetrated by a guide hole, plus a single surface depression of triangular shape and trapezoidal subsurface aspect incompletely penetrating the wall, on one side; (2) a Post, a long isosceles-triangular prism whose "large" and "small" ends are terminated by several fishhook fasteners, with the odd face penetrated at its center by a circular hole behind which lies a quarter-circle internal cavity; and (3) a Lock, an approximately h-shaped part with a circular rod emerging normal to the 3-junction, tipped with two fishhook fasteners mounted at an acute angle. The Post attaches the Screen to the Actuator, and the Lock attaches to the Post beneath the guide hole in the Screen.

Part P consists of a long cylindrical peg with a guide pin projected radially from the surface near one end. The pin is L-shaped in cross-section and fits into an L-shaped guide hole in the P-Screen. Part H is a rectangular housing with an interior hole large enough to admit Part P, and also has a guide pin projecting normal to its surface, also L-shaped but a mirror inverse of the Part-P pin fitting into an isomeric L-shaped guide hole in the H-Screen. Guide pins are made of a different material than the part, and may be chemically dissolved after all assembly operations are complete, leaving a clean final product. The hole in Part H may be blocked using a soluble plug that can be dissolved after parts binding but before parts insertion.

A part-insertion assembly cycle (Figure 3) proceeds as follows. A large number of Insertion Assemblers are placed in a hot liquid suspension containing a high concentration of parts P and H. All Actuators remain fully extended ("A"). The suspension is vigorously agitated using mechanical stirring, acoustic vibration, gaseous ebullition, oscillating magnetic fields, or by other means. Parts collide with each other, and with the assembler. By chance, some P-parts collide with an unoccupied P-Screen in an orientation that allows their guide pins to pass through the L-shaped guide hole; the guide pins of H-parts are excluded from this hole. Once partially inserted, the P-part is hammered further into the hole by subsequent external impacts until its guide pin strikes the base of the Lock, rotating the Lock and locking Part P in place, oriented coplanar with the Actuator axis ("B"). Similarly, H-parts soon fill the H-Screens, also locked in place, coplanar with the Actuator axis, and oriented with their opening facing Part P. The composition of the suspension fluid is adjusted to achieve neutral buoyancy for assemblers having two parts attached, and any excess parts are separated from the suspension by gentle centrifugation. If necessary, solvent is added to the suspension to dissolve soluble plugs that may be blocking H-part holes.

The remaining liquid suspension is then cooled, causing the actuator working fluid to condense; with a low internal pressure, each Actuator contracts, forcing part P toward Part H and inserting the cylindrical peg into the housing ("C"). When part P is fully inserted the kick bars on the opposing Locks move into contact, forcing both self-releasing Locks open. The cold liquid suspension is again agitated; assembled PH congeries (the product), no longer physically locked to the assembler, lift free into the suspension ("D"). The composition of the suspension fluid is again adjusted to achieve neutral buoyancy for empty assemblers, allowing the separation of pure PH congeries from suspension by gentle centrifugation. PH congeries are passed along to their next assembly step; after reheating, the assemblers are ready for another assembly cycle. Re-entry of product congeries into guide holes after detachment is prevented by the Screens which must extend at least as far beyond the guide hole as the distance between guide pins of an assembled congeries.

Thus the 8-part Insertion Assembler can perform linear insertion operations on any parts having mateable surfaces and configurations lying within the accessible work envelope of the device, and which have correctly shaped and positioned guide pins that identify them as valid parts.


5.2 The Rotation Assembler

Figure 4 shows a less-detailed schematic of the Rotation Assembler. The design ("A") is similar to the Insertion Assembler, except that the H-receptor is mounted orthogonal to the actuator axis, rather than collinear with the P-receptor as in the Insertion Assembler. The P-Lock is omitted, the P-Screen guide hole dimensions are enlarged by a factor of 21/2 to permit guide pin tilting by up to 45o during Part-P rotation, and the P-Post loses its hole and elongates to accommodate positioning requirements. A new kick bar is mounted on the side of the P-capsule, requiring an additional surface depression (of unique polygonal shape) in the P-capsule surface in order to position and secure the bar.

A part-rotation cycle (Figure 4) proceeds as follows. PH congeries are suspended in hot fluid along with the assemblers and are agitated. Correctly aligned congeries insert their pins through the P- and H-Screen guide holes, and the H-pins lock into place ("B"). Upon cooling, actuator contraction drags the P-pin counterclockwise, rotating Part P by 45o relative to Part H. As the Actuator reaches the end of its travel ("C"), the side-mounted kick bar unlocks the H-receptor; agitation followed by centrifugation releases ("D") and removes the rotated PH congeries from the suspension.


5.3 Assembler Self-Assembly Sequence

The 8 parts comprising the Insertion Assembler are fabricated by various conventional means as described earlier. The assemblers may then be sequentially self-assembled as follows.

First, P- and H-capsules are fabricated with capsule guide pins radially protruding from the site of the triangular surface depression. An assembly tube is fabricated consisting of a hollow cylinder slightly larger in diameter than the H-capsule, with an alignment channel grooved into the interior surface of the tube into which the capsule guide pins can entirely fit. A 50/50 random mixture of fluidborne P- and H-capsules are fed into the assembly tube from a feeder mechanism. Once the tube is filled, the contents are gently squeezed, forcing adjacent capsules to slide together and lock into place, giving up to a theoretical 25% maximum yield, plausibly with mean rotational alignment errors of ~1%. The tube is emptied, all completed bicapsular assemblies are extracted by centrifugation, and the guide pins are solvated away, leaving a population of completed actuators.

Next, the actuators are cooled, causing them to contract such that the H-capsule covers the triangular depression on the P-capsule surface. Only the H-capsule depression remains exposed. H-Posts are added to the suspension with vigorous agitation, irreversibly seating the H-Posts on the H-capsule wall in the correct orientation after a sufficient duration. (Posts are large on the Capsule end and small on the Screen end, hence the two ends may be positionally distinguished.) Excess Posts are removed by centrifugation. H-Locks are added to the suspension and agitated. The part seats at mid-Post and rotates into the stable quadrant after sufficient jostling; excess Locks are removed by centrifugation. H-Screens are added and agitated, adhering irreversibly with the fishhook latches at the ends of the Locks; excess parts are removed. Then the suspension is heated, revealing the still-vacant P-capsule triangular depression, and the above sequence is repeated to attach the P-receptor, piece by piece, to the P-capsule wall in the proper orientation. After final centrifugal purification, the suspension consists largely of completed functional Insertion Assemblers, ready to begin work.


5.4 More Complex Products and Assemblers

Kinematic-diffusion assemblers have numerous important drawbacks. First, assembly speed is limited by the time required for parts to diffuse into place before the assembly cycle may begin (see Section 6). This speed improves for smaller devices, hence nanoscale systems could take best advantage of this approach. Second, a lengthy sequence of events are required per assembly cycle, and only one assembly operation can be performed per assembly cycle with the current design. Third, each assembler is custom-built to perform just one specific assembly operation on one specific pair of parts, mimicking the high specificity of enzymes in biochemistry. Complex products consisting of N parts could require the design and construction of up to (N-1) different species of assemblers, although an optimally efficient assembly sequence could require as few as log2(N) distinct assembler species in the limiting case of two primitive part types. Fourth, assembly motions are unidimensional and work envelopes are quite limited. Fifth, all parts need coded handles for identification and alignment, requiring 3-dimensional control of parts fabrication. Sixth, actuators are so crudely assembled that working fluid will escape or become contaminated with suspension fluid after some unknown number of thermal cycles, whereupon the assembler may be discarded or recharged by pressure cycling in a bath of working fluid if the original capsule seals remain intact.

Despite these many drawbacks, kinematic-diffusion assemblers are good candidates for first-generation devices because they are simple to operate, are capable of self-assembly, and can be built and operated without any recourse to precision manipulation instrumentalities which are not yet available.

Assembler function may be varied within certain well-defined limits. For example, insertion distance or rotation angle between 0o and 45o is controlled by adjusting Screen position relative to the Post, guide hole position within the Screen, or kick-bar length on the Locks. Vertical insertion positioning may be adjusted by varying the length or shape of each Post. Guide holes of different shapes may allow multiple assembler species to operate on multiple part types simultaneously, although this could increase the risk of jamming; parts feedstock concentrations could be varied to dynamically control assembly sequences.

More complex configurations and procedures are needed to perform simultaneous three-part operations, more extreme single-axis rotations, or more complex multi-axis rotations. Rather than the one assembly workplane in the first-generation design, multiple assembly workplanes could be positioned along the actuator surface running parallel to the axis, permitting multiple simultaneous insertion operations. Guide pins of different compositions may be selectively dissolved during intermediate steps of the assembly process, giving some control over intermediate configurations. Second-generation assemblers can be constructed by connecting together several individual assemblers in various positions and orientations. A multi-actuator assembler could employ various internal working fluids that condense at different temperatures (Table 1), making possible the stepped control of multiple assembly operations on a single workpiece. By slowly lowering or raising the suspension fluid temperature through various boiling-point set points, more complex and repetitive assembly schedules can be sequentially performed upon a given workpiece. Power and control functions could also be driven by nonthermal pressure-driven multiplexed ultrasonic actuators in place of the bicapsular actuator; other assembler motive sources are readily imagined, such as kinesin transport on nanopatterned microtubule arrays or precision-perforated electrically-cycled piezocrystals. Still more sophisticated third-generation assemblers might be endowed with the ability to read and obey an executable data tape, making possible true programmable manufacturing.


6. Assembly Forces, Speeds, and Precision

The forces generated by a cooling actuator depend upon capsule size, ambient static pressure, the change in temperature, and the fluid employed. For a water-driven device, cooling from 100 oC to 90 oC produces a 0.3 atm drop in vapor pressure, increasing to 0.5 atm at 80 oC, 0.9 atm at 50 oC and 0.99 atm at 0 oC. Assuming a ~1 atm pressure differential, an actuator of ~1 micron2 cross-section produces ~100 nN of force, while a ~100 nm2 actuator produces ~10 pN of force -- sufficient to move the device through water at a Stokes Law velocity of up to ~0.1-1 m/sec, implying a 0.1-1 microsec actuation time. Higher forces may be applied if higher ambient pressures are employed.

However, parts will diffuse into place at a far slower pace, so assembly speed is limited by the mean parts reception time tpart ~ (Qhitpbind)-1, where the number of part-assembler impacts per second Qhit ~ vpart cpart1/3 for agitated parts of size Lpart in suspension at number density cpart moving at mean velocity vpart; the volume fraction of parts in suspension is f = cpart Lpart3. The probability that a part which impacts an assembler will bind at its parts receptor is roughly pbind ~ Ar ApDq 3, where Ar is the ratio of the receptor guide hole area to the total assembler surface area, Ap is the ratio of the part guide pin end tip area to the total part surface area, and Dq is the maximum fractional angular error on each of three rotational axes that will still allow guide pin insertion. If parts and assemblers are roughly of comparable size and number density, and taking Ar ~ Ap ~ 1/250, Dq ~ 5%, f ~ 10% and vpart ~ 1 m/sec, then tpart ~ 109Lpart ~ 1 sec for nanometer-scale parts, and tpart ~ 1000 sec for micron-scale parts. Thus assembly speed may be on the order of minutes per cycle for submicron parts, improving as scale is reduced. Even assuming only ~1% yield of correctly finished product congeries per assembly cycle with f ~ 10%, a reaction vessel containing one liter of suspension fluid deterministically produces ~1012 micron-scale PH congeries or ~1021 nanometer-scale PH congeries per assembly cycle.

First-generation kinematic-diffusion assemblers can only assemble structures whose design can tolerate initial insertional and rotational positioning errors of ~5%. For a 10-nm part, a 5% alignment error is only ~3 carbon atoms wide. However, atomically precise parts may incorporate guide tracks or channels, bumper knobs, asymmetrical apertures, or other fiducial features to allow self-correction of imprecise insertions, resulting in assembled congeries possessing greater positional precision than the physical structure of the assembler mechanism that assembled them.

Why not simply allow the feedstock parts to collisionally assemble, without benefit of the assembler? There are numerous reasons. First, randomly self-assembled parts may join or rotate into many different orientations with varying insertion depths, and there is no convenient way to separate out the desired configurmers after the fact; a deterministic assembler produces controllable and easily recovered high concentrations of desired configurmer. Second, an assembler may apply much higher insertion or rotation forces than random collisions, allowing the assembly of configurmers that are far from equilibrium. Third, the use of parts handles allows complex congeries containing many parts of similar size and shape to be readily distinguished before, during and after assembly. Fourth, the ability to flush excess parts immediately prior to the assembly operation, and to separate product from assembler after the assembly operation, greatly improves recoverable product yield.

The mechanical mating of dissimilar submicron parts into hybrid devices in a fluid environment, using complementary DNA strands as part of a "fluidic self-assembly" assembler mechanism affixed to a silicon surface, has recently been reported [16] by a group at UCSD led by Sadik Esener.


7. Conclusions

Past attempts to define a first-generation molecular assembler have assumed that a machine capable of both assembly and fabrication will be required. However, a machine that is capable of assembly alone can replicate itself from a limited set of input materials, and can be extremely simple both in structure and function. This insight has led to the conception of a new class of manufacturing systems called kinematic-diffusion assemblers that can be fabricated today and could in principle serve as first-generation submicron-scale molecular assemblers.

A vast number of assemblies cannot be manufactured by this primitive first-generation system. However, a small but significant number of assemblies can be manufactured, including but not limited to the device itself. Operation can be sequential, hence components of significantly greater complexity than the original assembler can be constructed. Atomically precise parts may incorporate fiducial features to allow self-correction of imprecise insertions, hence assembled congeries possessing greater positional precision than the physical structure of the original assembler can be constructed. Assembly speeds may be on the order of minutes per cycle for submicron parts, improving at smaller scales. These results support the inference that second-generation assemblers of greater functional diversity and positional precision could also be manufactured using the kinematic-diffusion approach.



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Last updated on 2 November 2002