Duke University

The Magic of Self-Replication

Yuanhao Guan

Math 89S: Mathematics of the Universe

Professor Hubert Bray

October 2016

Abstract

In this paper, the idea of self-replicating is analyzed and a particular kind of self-replicating

robots(SRRs) is reviewed. The key issues that will determine the feasibility of actually creating

robots that can evolve and reproduce are also evaluated. In addition, this paper is not restricted to

active mechanical replication. Applications in biology, computer science, chemistry are going to

be discussed as well.

Keyword: self-replication, robots, Quine, von Neumann, RepRap

1.Introduction

In this paper we review several applications of self-replication in different fields. Self-

replication is an essential feature in the definition of living things. In this paper, we will stick to

this definition: ‘a self-reproducing organizational form constructing itself in a simple

environment and capable of evolution’. At the core of biological self-replication lies the fact that

nucleic acids (in particular DNAs) can produce copies of themselves when the required chemical

building blocks and catalysts are present. This self-replication at the molecular level gives rise to

reproduction in the natural world on length scales ranging the ten orders of magnitude from 10-8

meters to 102 meters. Not all of the machinery involved in biological self-replication is fully

understood, and remains a subject of intensive interest. Self-replication in non-biological

contexts has been investigated as well, but to a much lesser degree. [1] Any self-replicating

mechanism which does not make a perfect copy will experience genetic variation and will create

variants of itself. These variants will be subject to natural selection, since some will be better at

surviving in their current environment than others and will out-breed them. [2] Thus, self-

replication gives us the chance to use Darwinism to create basic AI and even robots that can be

called “artificial life”.

2.Self-replication in Computer Programming

Anyone who use Microsoft 98 back in 90s and 00s would know how destructive a computer

virus can possibly be. There’s no way for an antivirus software to uncover all computer viruses

and they cause billions of dollars’ worth of economic damage each year. In essence, a computer

virus is just a malicious software program that is capable of replicate itself. It is known as the

“quine”—a non-empty computer program takes no input and produces a copy of its own source

code as its only output. With a few modifications, these “quines” are able to self-replicate and

install themselves without user consent.

Fig.1 (An example Quine by java)

Computer viruses has been around for quite a while. It is truly a nightmare: they can wipe

out the information on a hard drive, turn a CPU into a useless piece of metal, and even turn your

machine into a ‘zombie’ which can replicate themselves and send to other computers. However,

the history of computer viruses might be longer than you think. In 1949, less than a decade after

the invention of computer, a scientist named John von Neumann theorized a self-replicated

program was possible. (It did take a few more decades for hackers to begin building computer

viruses, though) [3] In talk.origins, Zoe Althrop wrote: “if you can show me a program that is

acknowledged to be a program, and this program does not have a programmer, then my

hypothesis will be falsified.” A computer virus would then qualify to blow her mind: it is a

program itself, and it is capable of reproduce itself. With a few modifications, computer virus

can even evolve: each “offspring” it has is a slightly different from the parent program. (Of

course 99 percent of the time, these “offspring” would fail to compile) As a hacker, you only

need to write the original virus file and grant it the ability of reproducing; then, all you need to

do is just wait for it to spread and breed. Clearly Zoe’s hypothesis doesn’t hold today. Anyone

who has witnessed the destruction of a massive network would feel the power of applying self-

replication in computer programming.

(An example of creating a computer virus in C language: when executed it creates a copy of

itself in all the other files in the same directory)

3.Self-replication in Mechanics

The concept of artificial self-replicating systems was originated by von Neumann in the 1950s

in his theory of automata. Using a theorem invented by Turing in 1937, Neumann was able to

infer that the construction of an automatic machine capable of replicating itself was possible. The

main problem is that, instead of being able to read and write data, a self-replicating system reads

instructions and converts these into assembly commands that result in the assembly of replicas of

the original machine together with a copy of the assembly instructions (so that the replica also

has the ability to replicate). Although the vast majority of work in non-biological self-replicating

field is in the form of non-physical self-replicating automata (e.g., computer viruses we

mentioned earlier, etc.), these works do provide an existence proof for non-biological self-

replication. [4]

3.1. Principle of Self-Replicating Robots

According to their behavior, self-replicating robots can be categorized into two primary

divisions. In short, ‘directly replicating robots’ are robots that are capable of producing an exact

replica of itself in one generation, and robots capable of producing one or more intermediate

robots that are in turn capable of producing replicas of the originals are called “indirectly

replicating robots”. [12]

3.1.1 Directly Replicating Robots

Directly replicating also refers to Autotrophic self-reproduction or self-replication: The ability

of a system to make a direct copy of itself from raw materials without assistance. As yet, no

artificial autotrophic self-reproducing kinematic machine has been made. However, examples

exist in biology (see Section 2). [4] For a kinematic machine to achieve autotrophic self-

reproduction, it must contain a number of critical subsystems. One attempt to identify these

subsystems was undertaken in Freitas and Merkle’s “Map of the Kinematic Replicator Design

Space” in their comprehensive book, which identified 137 design properties in order for

autotrophic self-reproduction to be possible. [5]

As mentioned earlier, the first person to formalize thoughts on the subject was von Neumann

in the middle of the last century. Much of von Neumann’s work concentrated on his cellular

machine, a theoretical and mathematical model, and records of his research into a kinematic

(physical) self-reproducing machine are scarce and often informal. [7] Much of the outline

presented here is based on the summary in the review by Freitas and Merkle.2 Von Neumann’s

kinematic reproducer, as illustrated by Cairns-Smith4 in Fig. 1, consists of five distinct

components, namely a chassis (c), a set of instructions (I), some form of machinery (m), a

controller (r) and, finally, a sequencer (s). In order for the kinematic reproducer to function

properly, it is required that it resides in a stockroom containing an unlimited quantity of spare

parts. [11] The kinematic machine features a mechanical appendage that is able to gather parts at

random from this stockroom; the randomly selected part is inspected and compared with the

kinematic machine’s instructions. In the event that the part is not required, it is replaced in the

stock room and the process is repeated until a required part is found. This process is then

repeated to find the next required part, and the two parts are connected together using the

mechanical appendage. This cycle continues until a physical copy of the kinematic machine is

produced; at which point, the instructions are copied in to the memory in the child kinematic

machine before it is finally activated. [9]

Fig. 3. Schematic of von Neumann’s kinematic reproducer from

Some of the most elegant work into self-assembling kinematic machines using special pre-

made parts was conducted by Roger and Lionel Penrose in designing their so-called block

reproducers. 6 Perhaps the biggest achievements of their design are its neatness and simplicity.

The block reproducer (Fig.3) consists of a series of wooden blocks that are placed on an

agitating surface. The design of the blocks is such that an interlocking profile exists on each

block. [8]

Fig.3 A 1-D self-reproducing kinematic machine made from parts of two kinds from ref 1

“Brownian-motion” is induced into the parts by agitating the surface, enabling the locking

profile to be utilized for completing the assembly process. The Penroses also designed a more

complicated two-dimensional reproducing kinematic machine along similar lines.

Further work into self-assembling processes was conducted by Moses, who developed a self-

assembling kinematic machine in the form of a Cartesian manipulator based on 16 types of snap-

fit parts. Similar to von Neumann’s kinematic reproducer, it was able to build a copy of itself if

supplied with sufficient parts. However, whilst the concept proved promising, the structure of the

design lacked stiffness, leading the machine to need external assistance to complete its

reproduction cycle. But, inspired by this success, the world’s first semi-autonomous, limitedpart,

self-assembling kinematic machine was created in 2003 by Suthakorn et al., with an assembly

time of just 135 s. It consisted of an original robot, subsystems of three assembly stations and a

set of subsystems from which replicas of the original robot were assembled. In 2005, Zykov et

al. made a system consisting of cubes split along a diagonal where each half-cube could rotate

relative to the other in that split plane. The cube’s faces were fitted with electromagnets. Stacks

and other arrangements of these could be made to reproduce themselves if fed with a supply of

similar active cubes, with the stack acting as a robot arm when the split faces were rotated.

However, the machine cannot manufacture individual cubes, nor do they occur naturally, so its

status as a self-replicator is debatable. [7]

3.1.2 Indirectly Replicating Robots

The primary characteristic of the robots in this division is that the original robot or

group of robots work together to build a robot-producing factory or some type of

intermediate robot which is able to produce replicas of the original robot. However,

the original robots lack the ability to directly assemble copies of themselves.[6]

Fig.4 The Block diagram of the categorization of self-replicating robots.

3.1.2.1 The RepRap Project

The most famous project in the field of directly replicating robots is probably the RepRap

project (RepRap is short for replicating rapid prototyper.). started as a University of Bath

initiative to develop a 3D printer that can print most of its own components and be a low-cost 3D

printer, but it is now made up of hundreds of collaborators worldwide. [9] Due to the ability of

the machine to make some of its own parts, authors envisioned the possibility of cheap RepRap

units, enabling the manufacture of complex products without the need for extensive industrial

infrastructure. They intended for the RepRap to demonstrate evolution in this process as well as

for it to increase in number exponentially.

Fig.5 RepRap version I “Darwin”. This is the first production RepRap machine.

This self-reproducing kinematic machine is really special-contrary to what people usually

think of self-replicating machines, RepPap is designed to manufacture a kit of parts for a copy of

itself, and to need the assistance of people to assemble that copy. Doesn’t sounds really

interesting, right? What if I told you that it can make people all manner of useful products when

not producing? It seemed (and still seems) likely that this would lead to a mutualist relationship

between people and the machine that would inherit some of the longevity and the robustness of

the evolutionarily stable strategies of the insects and the flowering plants.

On 13 September 2006, the RepRap 0.2 prototype successfully printed the first part of itself,

which were subsequently used to replace an identical part originally created by a commercial 3D

printer. On 9 February 2008, RepRap 1.0 "Darwin" successfully made at least one instance of

over half its total rapid-prototyped parts. On 14 April 2008, possibly the first end-user item is

made by a RepRap: a clamp to hold an iPod securely to the dashboard of a Ford Fiesta. By

September of that year it was reported that at least 100 copies have been produced in various

countries. Lately, the authors and their many RepRap colleagues around the world have now

finished the design and commissioning of the latest RepRap machine: RepRap Version II

“Mendel”. The percentage of the machine that “Mendel” makes for itself has remained constant

in comparison to “Darwin”, despite a significant number of rolling element bearings being

incorporated into the design to give robustness. Furthermore, some users in the community have

replaced these bearings with plain bearings. In this case, the self-manufactured percentage rises

to 57%. It is anticipated that the number of self-manufactured parts will rise further once the

multiple write-heads are finished. We have reasons to believe that in the future, the percentage

will rise to at least 80%. [10]

Fig.6 RepRap Version II “Mendel”. This version is smaller, lighter and simpler than Version I,

but it has a larger build volume.

Fig.7 Comparison of “Darwin” and “Mendel”

4. Conclusion

The Construction of various types of machines and programs which can automatically self-

replicating, in a sense derived from von Neumann, has been outlined. Although self-replication

has demonstrated its power in biology and computer programming, it’s application is limited and

restricted in other fields. However, self-replication is still a topic that worth focusing on, since

we can expect all sorts of magical stuff it can do. For example, it has been suggested that no

large-scale nanotechnology industry can develop without self-replication. Nobody would doubt

the miracles self-replication can do for us in the future. After all, every single one of us is a great

master-piece of self-replication.

Reference:

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(http://vx.netlux.org/lib/ mlp01.html)

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