Evolution-in-materio: Evolving computation in materials

Abstract

Evolution-in-materio (EIM) is the manipulation of a physical system by computer controlled evolution (CCE). It takes the position that to obtain useful functions from a physical system one needs to apply highly specific physical signals and place the system in a particular physical state. It argues that CCE is an effective methodology for doing this. One of the potential advantages of this is that artificial evolution can potentially exploit physical effects that are either too complex to understand or hitherto unknown. EIM is most commonly used as a methodology for implementing computation in physical systems. The method is a hybrid of analogue and classical computation in that it uses classical computers to program physical systems or analogue devices. Thus far EIM has only been attempted in a rather limited set of physical and chemical systems. This review paper examines past work related to EIM and discusses historical underpinnings behind such work. It describes latest developments, gives an analysis of the advantages and disadvantages of such work and the challenges that still remain.

Full text

Evolutionary Intelligence Special Issue: new emerging areas manuscript No.
(will be inserted by the editor)
Evolution-in-materio: evolving computation in
materials
Julian F. Miller ·Simon L. Harding ·
Gunnar Tufte
Received: date / Accepted: date
Abstract Evolution-in-materio (EIM) is the manipulation of a physical sys-
tem by computer controlled evolution (CCE). It takes the position that to ob-
tain useful functions from a physical system one needs to apply highly specific
physical signals and place the system in a particular physical state. It argues
that CCE is an effective methodology for doing this. One of the potential
advantages of this is that artificial evolution can potentially exploit physical
effects that are either too complex to understand or hitherto unknown. EIM is
most commonly used as a methodology for implementing computation in phys-
ical systems. The method is a hybrid of analogue and classical computation in
that it uses classical computers to program physical systems or analogue de-
vices. Thus far EIM has only been attempted in a rather limited set of physical
and chemical systems. This review paper examines past work related to EIM
and discusses historical underpinnings behind such work. It describes latest
developments, gives an analysis of the advantages and disadvantages of such
work and the challenges that still remain.
Keywords evolutionary algorithms ·material computation ·evolvable
hardware
Julian F. Miller
Department of Electronics, University of York, Heslington, York, UK, YO10 5DD
Tel.: +44 (0)1904 32 2383
Fax: +44 (0)1904 32 2335
E-mail: julian.miller@york.ac.uk
Simon L. Harding
Department of Electronics, University of York, Heslington, York, UK, YO10 5DD
E-mail: slh@evolutioninmaterio.com
Gunnar Tufte
Department of Computer and Information Science, Norwegian University of Science and
Technology, 7491 Trondheim, Norway
Tel: +47 73590356
E-mail: gunnar.tufte@idi.ntnu.no

2 Julian F. Miller et al.
1 Introduction
Natural evolution can be looked at as a physically instantiated algorithm that
exploits the physical properties of materials. It is not principled since there is
no designer who constructs living systems from simpler and well-understood
components. This way of constructing things is in marked contrast to the way
human beings design useful systems. Human designers refine useful building
blocks and combine these in highly constrained ways to arrive at solutions to
problems. This paper is concerned with attempts to use computer controlled
evolution to ‘program’ useful devices by allowing artificial evolution to directly
manipulate a physical system. In this way it is hoped to create novel and useful
devices in physical systems whose operational principles are hitherto unknown.
We tentatively suggest that it will not be possible to construct compu-
tational systems of equivalent power to living organisms using conventional
methods that employ purely symbolic methods. We argue that it will be ad-
vantageous for complex software systems of the future to utilize physical effects
and use some form of search process akin to natural evolution.
Evolution-in-materio (EIM) is a term that refers to the manipulation of
physical systems using computer controlled evolution (CCE) [35–37,53]. It
is usually thought of as a kind of unconstrained evolution in which by the
application of physical signals various intrinsic properties of a material can be
heightened or configured so that a useful computational function is achieved.
Yoshihito discussed a closely related concept of “material processors” which
he describes as material systems that can process information by using the
properties of the material [102]. Zauner describes a closely related term which
he calls “informed matter” [103].
The concept of EIM grew out of work that arose in a sub-field of evo-
lutionary computation called evolvable hardware [30,38, 76, 104] particulary
through the work of Adrian Thompson [86,91]. In 1996, Thompson famously
demonstrated that unconstrained evolution on a silicon chip called a Field
Programmable Gate Array (FPGA) could utilize the physical properties of
the chip to solve computational problems [85]. We discuss this and related
work in Sect. 9 of this paper.
Interestingly, close inspection of much earlier research publications (see
Sect. 3) reveals that similar ideas, albeit without computers, were conceived in
the late 1950s (particularly by Gordon Pask [63]). In Sect. 6 we discuss Gordon
Pask’s 1958 work using ferrous sulphate solutions. Evolving computational
solutions in other chemical systems has also been achieved, particularly using
reaction–diffusion systems. We discuss this in Sect. 11.
Indeed, it is also noteworthy that two of the pioneers of evolutionary com-
putation Ingo Rechenburg and Hans-Paul Schwefel came to invent the evolu-
tionary strategy algorithm through a process of trying to manipulate a physical
device [69,75]. The device in question, known as an “Experimentum Crucis”
was a series of six planar plates that could be positioned at various angles
to one another via adjustable hinges. They wanted to minimize the air flow
drag across the plate. Using what later became known as a (1+1) evolution-

Evolution-in-materio computation 3
ary strategy, they made small random changes to the angles and examined the
airflow.
Despite this early pioneering work in the evolution of physical devices, the
field of evolutionary computation has largely concerned itself with evolution
in simulo, which refers to the evolution of computer models of physical sys-
tems. The reason for this is simple, evolutionary algorithms generally consider
many possible solutions to problems in order to converge on a sufficiently sat-
isfactory optimum. In this situation, including “hardware-in-the-loop” is not
often feasible, due to the time taken to manipulate the physical system and
make an assessment of a potential solution’s quality. Since then, computers
and computer control systems have become more powerful and sophisticated,
this has allowed some physical devices to be manipulated sufficiently quickly
for evolution-in-materio to become possible. We review attempts to cross the
“reality gap” between simulation of physical objects to evolving buildable de-
signs in Sect. 8.
Eiben et al. [25] discuss what they term “Embodied Artificial Evolution”
(EAE) in which evolutionary operators operate in physical space, that is to say
the entire algorithm and products of evolution are embodied. They identify
three kinds of artificial evolution. In the first kind the evolutionary algorithm
and the products are digital, there is no physical artefact produced. Evolution-
ary optimization, data modeling, simulations etc. fall in this category. In the
second kind, the evolution designs a physical artefact (or at least something
that could be realised physically), so that something could be constructed af-
ter the evolutionary process has finished. In the third kind, the evolutionary
process itself and the products of evolution are physical. Directed evolution,
in which human beings have intervened in natural evolutionary processes by
mutating, recombining and selecting naturally occurring systems (chemicals,
enzymes and bacteria) is an example of EAE [73]. They argue that the devel-
opment of a variety of technologies have made it possible to implement EAE,
these include rapid prototyping and modular robotics.
We argue that there is an important stage between the EAE levels 2 and 3,
this is where evolution designs a physical artefact which is assessed in situ (i.e.
during evolution). So all the evolved designs are embodied however the evolu-
tionary operators still take place inside a computer. This is where most work in
evolution-in-materio sits. We refer to this as “embodiment level 2.5.” In some
systems, the actual evolutionary algorithm may be built in hardware, however
usually this is for reasons of computational efficiency or physical compact-
ness. The evolutionary algorithm though operating in purpose built hardware,
is functioning in a similar way to an algorithm running on an off-the-shelf
computer. Eiben et al.’s level 3 refers to physical systems that are building
themselves, so that artefacts are created and destroyed, mutated and recom-
bined.
In EAE the emphasis is on construction. Physical entities are constructed,
pass on their genetic material to offspring which are constructed. Through
variation, reproduction and selection a form of physically realised evolution
takes place. However, in EIM in most cases, the emphasis is on computation

4 Julian F. Miller et al.
although it does include cases where the aim is to obtain physical or chemical
systems with desired properties (these are discussed in Sect. 13).
The purpose of this paper is to discuss evolution-in-materio, work that
relates to it, and finally to update the reader on the latest developments.
Most of the published work we discuss in this paper lies at EA level 2.5. There
is a great breadth of work done at this level, and we discuss work in fields
as diverse as electronic circuit design, analogue computing, antenna design,
chemical computation, protein and enzyme computing, and vesicle design.
One of the exciting aspects of evolution-in-materio is that it has the po-
tential to discover new modalities of operation, new physical variables and in-
teractions that can be useful in solving a variety of problems. Evolved systems
also have the possibility of offering insights and understanding of exploitable
physical processes (in their most general sense) that are hitherto unknown.
Using approaches such as artificial curiosity, we may be able to find the prob-
lems that are best solved using evolution in materio even if we do not yet know
what the problem, or problem types, are [74].
A strong theme in evolution-in-materio is the evolution of novel forms of
computation. It appears to be a methodology that has promise in building new
kinds of analogue computing devices. Evolution is used as the programming
methodology. If unknown physical properties and interactions are to be utilized
in a computer program, it is obvious that the the program cannot be designed
in advance. An evolutionary algorithm together with a fitness function rewards
those configurations of the system that provide the desired computational
response. To some extent, we can see the program itself as “emergent”, since
it is not known in advance and emerges during the evolutionary process.
In section 4 we discuss briefly classical computation and its relation to
physics. This is important as EIM uses physical effects and interactions whereas
classical computation is based on the concept of a Turing machine in which
physics has at best a minor role.
Evolution-in-materio when used in a computational context is a form of
analogue computation. Sect. 5 discusses analogue computation and its the-
oretical foundations. It is interesting to note that Jon Mills’s (see Sect. 7)
Kirchoff-Lukasiewicz machine arose from Rubel’s theoretical definition of an
analogue computer that is itself potentially more powerful than Shannon’s
definition of a general purpose analogue computer.
In a paper in 2002, Miller and Downing coined the term “evolution-in-
materio” and suggested a number of physical systems that look both feasible
and promising. One of their suggestions was liquid crystal. This led to the work
of Harding et al. which demonstrates that it was possible to evolve configu-
rations of liquid crystal so that a liquid crystal display could perform various
kinds of computation. This is described in more detail in Section 10.
We also discuss other materials systems where evolution has been used in
Sections 13 and 12. In particular, Sect. 12 discusses work showing how nuclear
magnetic resonance can be used to carry out classical computation (as opposed
to the more usual quantum computation) and how robust logic gates can be

Evolution-in-materio computation 5
evolved. Sect. 13 discusses work where an evolutionary algorithm was used to
find mixtures of chemicals that had high turbidity.
We review briefly what kinds of materials are most suitable for evolution-
in-materio in Sect. 14. We also discuss an EU funded project which aims to
extensively investigate what kinds of materials are suitable for evolution-in-
materio and also what types of computation problems can be solved.
In Sect, 15 we discuss strengths and weaknesses associated with using mate-
rials in the evolutionary loop. The paper ends with conclusions and suggestions
for further work.
We begin with an overview of the concept of evolution-in-materio. We have
tried to be as general as possible so that this depiction encompasses all the
various ways that evolution-in-materio may be achieved.
2 Conceptual overview of evolution-in-materio
The central idea of evolution-in-materio is that the application of some phys-
ical signals to a material (configuration variables) can cause it to alter how it
responds to an applied physical input signal and how it generates a measur-
able physical output (see Figure 1). Physical outputs from the material are
converted to output data and a numerical fitness score is assigned depending
on how close a given function of the output data is to that desired. This fitness
is assigned to the member of the population that supplied the configuration
instructions. Ideally, the material would be able to be reset before the applica-
tion of new configuration instructions. This is important as without the ability
to reset the material it may retain a memory from past configurations, this
could lead to the same configuration having different fitness values depending
on the history of interactions with the material. We will discuss these advan-
tages and disadvantages in more detail in section 15. We refer to a material
that has been configured to perform computation as a configurable analogue
processor (CAP). For an alternative depiction of a CAP as a FPMA (field
programmable matter array) see [53].
A form of CAP is currently being developed in a European FP7-ICT re-
search project called NASCENCE (Nanoscale Engineering for Novel Compu-
tation Using Evolution) [15]. In this project a group of researchers are inves-
tigating evolution-in-materio using microlectrode arrays. The microelectrode
arrays can be covered with a variety of physical materials (see Sect. 14 for
details). In this kind of CAP, the physical inputs are voltages applied to elec-
trodes. The physical output are a number of voltages detected at designated
output electrodes. The physical configuration is another set of voltages that
are applied to electrodes. An evolutionary algorithm decides which electrodes
should receive input, output or configuration voltages. With this arrangement
it is possible to attempt to solve many well known computational problems.
Let us examine a couple of examples.
Suppose that one wishes to use such a CAP to solve a classification prob-
lem. In such problems there are a set of input variables (which we assume here

6 Julian F. Miller et al.
Fig. 1: Concept of evolution-in-materio. There are two domains: physical and
computer. In the physical domain there is a material to which physical signals
can be applied or measured. These signals are either input signals, output
signals or configuration instructions. A computer controls the application of
physical inputs applied to the material, the reading of physical signals from the
material and the application to the material of other physical inputs known
as physical configurations. A genotype of numerical data is held on the com-
puter and is transformed into configuration instructions. The genotypes are
subject to an evolutionary algorithm. Physical output signals are read from
the material and converted to output data in the computer. A fitness value is
obtained from the output data and supplied as a fitness of a genotype to the
evolutionary algorithm.
to be real numbers) and a number of classes to which particular instances of
input variables belong. On a computer a mapping is created that maps input
variables to voltages to be applied to the electrode array. A set of configura-
tion voltages are applied to the electrode array (to electrodes distinct from
the electrodes designated as input or output electrodes). The voltages at the
output electrodes are measured. On the computer a mapping is created that
associates a class with a particular output electrode. The electrode with the
largest measured output voltage defines the class of the input instance. The
genotype of the evolutionary algorithm is a set of numbers that define config-

Evolution-in-materio computation 7
uration voltages, the electrodes to which these voltages should be applied and
the electrodes which will be used as outputs.
Another computational problem that can be attempted with this approach
is the Travelling Salesman problem (TSP). Here one wishes to find the min-
imum length tour that visits a collection of cities. A solution can be repre-
sented by a permutation of the cities. Such a problem is easily mapped onto
an electrode array. In this case there are no input electrodes, only output and
configuration electrodes. One allocates as many output electrodes as there are
cities. The objective is to obtain a set of output voltages which can be mapped
into a permutation of cities. This can easily be done as follows. Denote the
voltages measured on the output electrodes by Vi. On the computer a two
dimensional array aij, is defined (see Eqn. 1).
aij =Vij= 0
i j = 1 (1)
So ai0holds the measured output voltages and ai1holds the identity per-
mutation. If the array elements ai0are sorted, one can read off a permutation,
in ai1. For example in a six-city problem one might record the following output
voltages, Vi0:
0.72 0.15 0.91 0.23 0.54 0.03
012345
After sorting by the first dimension we obtain
0.03 0.15 0.23 0.54 0.72 0.91
513402
It is clear from this discussion that many computational problems can
be attempted using an electrode array device. It remains to be seen whether
solutions to a variety of computational problems can be efficiently evolved
using this methodology.
Although “evolution-in-materio” arose relatively recently, it is interesting
to note that many of the underlying ideas arose much earlier in the cybernetics
community. We review briefly some of these ideas and the main contributors
in the next section.
3 Pioneers of ideas related to evolution-in-materio
Gordon Pask’s remarkable work in 1958 on electrochemical devices [63] is often
cited as one of the pioneering works of evolution-in-materio (We discuss this in
Sect. 6). However, Pask’s work can be seen as a result of collective information
and knowledge gathering that took place in the cybernetic movement.
The cybernetic community emerged mostly in Britain, through the Ratio
club [42], and in USA, through the Macy conferences [66], and coincided in
time with the development of the concept of stored program computers [61].

8 Julian F. Miller et al.
However, the cybernetic community also pursued alternative views on infor-
mation processing in machines (and animals/brains) and pioneered physical
computation in terms of philosophy, theory and experimental work. Even be-
fore the term cybernetics was coined by Wiener[101] the US cybernetic com-
munity was inspired by the largest most complex evolved physical information
processing device; the brain. Adaptation and learning in context of feedback
loops was the dominant theme. The goals were multitudinous, spanning from
understanding neurophysiology to devising self replicating machines, e.g. Mc-
Culloch and Pitt’s proposal on how networks of neurons could compute logical
functions [52] and von Neumann’s self-replicating automata [17].
The earliest work may not much resemble modern nanoscale [15] or biology
based [3] physical computational devices, but important ideas regarding com-
putational devices, complex systems, emergence and adaptation were sketched
out. At the time, adaptation, not evolution, was the main technique suggested
for exploring computation (or control).
The British branch of cyberneticians is especially interesting in the context
of evolution-in-materio. Adaptation and the brain were the main topics, this
was not unexpected since several had a background in medicine or psychia-
try [68]. This background led to a view of the brain as a kind of “black box”
that, if successfully opened, could be understood. Such a view opened the way
for thinking of electromechanical physical computation devices as models for
various brain and physiological processes. These early models are connected
to the notion of evolution-in-materio in various ways. Like the brain they were
trying to explore a potential behaviour (computational capability) which was
not known in advance. The atomic units of the system were simple, e.g. a few
vacuum tubes, not capable of expressing complex computational behaviour on
their own. The behaviour or computation of the systems was a result of several
units influencing on each other.
The role and idea of adaptation in the cybernetic community turns out
to be quite similar to the idea of using computer controlled evolution in
evolution-in-materio. W. Gray Walter’s tortoise-like robots [99] were three
wheeled robots that could turn the front drive wheel. The controller included
only a few vacuum tubes (or two neurons) and a light sensor. The robot
controller was hardwired to search for and approach light sources in its envi-
ronment. The point in relation to evolution-in-materio does not concern the
robots themselves, but rather the richness of behaviour and the unexpected
life–like behaviour that was found by search and emerged from what was con-
sidered a simple physical system interacting in an environment. The brain
and adaptation was also the main interest of W. Ross Ashby, as indicated
by his most well-known book “Design for a Brain” [7]. His famous machine;
the homoestat, demonstrated in the late 1940s, was an analogue and digital
mixed signal machine consisting of several interconnected electromechanical
units that could communicate and show collective adaptive behaviour. The
homeostat demonstrated adaptation, i.e. retaining and re-establishing stabil-
ity by trial and error. As with Walter’s tortoises, the machine itself is not our
main interest. However, one design property of Ashby’s homeostat should be

Evolution-in-materio computation 9
emphasized in the context of evolution-in-materio; a mix of analogue control
and digital state representation. The mixed signal approach may be a design
choice to quantify the number of system states from the richness of analogue
processing [20]. This mix of analogue operation and digital state representation
can be recognized in evolution-in-materio, e.g. Evolution in silico (Section 9)
and Liquid Crystal (Section 10).
Gordon Pask and Stafford Beer were second generation British cyberneti-
cians [68]. They did not share the strong connection to psychiatry of many
of their fellows. Their machines were aimed at exploring computation rather
than the simulation of brain and its physiological properties. Beer’s approach
to a physical computational system was related to operational research. Beer
sought, in good cybernetic spirit, to automate control of factories and compa-
nies. Beer’s approach was, as with Walter and Ashby, based on adaptation. In
his approach to achieving automatic production, the factory and its control
(management) was viewed as an adaptive system adapting to the demands
and resources available. He noted that the complexity of such a task was high,
in his words, ”exceedingly high”.
Beer concluded that great complexity was essentially probabilistic in na-
ture and therefore a probabilistic control system was required. There is not
much detail on Beer’s approach, but an adaptive biological computer was at-
tempted. Based on ecosystems (in a tank) consisting of fish which had be fed
iron particles interacting by electromagnetism and light [9]. Beers’s biologi-
cal computer experiments were not successful, but his reflections on the great
complexity of the system and its task suggested that the brain as a “black
box” could not usefully be opened and understood in detail [10]. This lack of
comprehensibility appears to be shared by many of the evolution-in-materio
systems (see in particular Section 9).
Beer also collaborated with Gordon Pask on electrochemical devices [63].
Pask’s work is close to evolution-in-materio and described in detail in Section 6.
However, in relation to cybernetics the use of trail and error as the search for a
computational device should be noted. Pask used a process of trial and error,
adjusting voltages in a ferrous-sulphate device in order to grow “dendrites”
which was similar to the (1+1) evolutionary strategy devised by Rechenburg
and Schwefel’s (see Sect. 1). Pask continued the theme of adaptation started
by Wiener, Walter and Ashby. However, in contrast to the first generation of
cyberneticians Pask did not aim at opening the brain ”black box”, he wanted
to construct computational machines beyond conventional computers. He later
named such machines “Maverick Machines” [64].
A project with similarities to Pask’s electrochemical device is the Linear
Field Trainable (LIFT) experimental electrochemical system by Stewart [79].
Stewart pointed out several properties valid for evolution-in-materio; a system
can not be opened and inspected, even a part count may not be possible. A
”bulk” production process may be required, similar to a bakery, manufacturing
”logic by the pound”. The proposed production method is especially interest-
ing. Stewart proposed to stimulate machines in a similar way to the way in
which modern programmable chips such as FPGAs are configured. Further,

10 Julian F. Miller et al.
Stewart proposed that the machines should be a grid of metallic structures
where the functionality is defined by learning and adaptation. Stewart’s de-
vice was based on iron or gold particles in nitric acid placed in high pressure
(100 - 2000 psi) containers. LIFT was designed to be a pattern recognition
system. In a similar manner to that used by Pask, electrical stimuli were ap-
plied in a process of trial and error, gradually stimulating the system toward
the goal. LIFT, as with Pask’s device, enforces growth of structures. However,
the goal of LIFT was to be able to produce several different behaviours, i.e.
threshold functions, by learning in reconfigurable matter.
In all the early work presented adaptation and learning provided the ex-
ploratory force. However, evolution itself can be considered as adaptation.
For example, Holland [39] links biological properties, i.e. growth, control and
neurophysiology, with Von Neumann’s self-reproducing automata and popu-
lation based adaptation. Coupling the experimental cybernetic machines with
evolution, i.e. evolution-in-materio.
4 Classical computation and physics
One of the main aims of evolution-in-materio is to evolve new kinds of compu-
tational devices by exploiting physical interactions in material systems. How
does this relate to classical computation?
Classical computation is based on an abstract model of a machine called a
Turing Machine [97]. Such a machine can write or erase symbols on a possibly
infinite one dimensional tape. Its actions are determined by a table of instruc-
tions that determine what the machine will write on the tape (by moving one
square left or right) given its state (stored in a state register) and the symbol
on the tape. Turing showed that the calculations that could be performed on
such a machine accord with the notion of computation in mathematics. The
Turing machine is an abstraction and it remains unclear what limitations or
extensions to the computational power of Turing’s model might be possible
using real physical processes. Von Neumann and others at the Institute for
Advanced Study at Princeton devised a design for a computer architecture
based on the ideas of Turing that formed the foundation of modern stored
programs computers. These are digital in operation. Although they are made
of physical devices (i.e. transistors), computations are made on the basis of
whether a voltage is above or below some threshold. Classical computers are
based on a symbolic notion of computation.
We can view the Turing machine in the context of evolution-in-materio as
discussed in the Section 2. The configurable material is the tape. The physical
input is the writing of symbols on the tape. The physical output is the reading
of symbols on the tape. The tape is a passive storage medium which does not
have physical properties that can be exploited.
Interestingly, the degree to which the underlying physics affects both the
abstract notion of computation and its tractability has been brought to promi-
nence through the discovery of quantum computation. Deutsch pointed out

Evolution-in-materio computation 11
that Turing machines implicitly use assumptions based on physics [24]. Other
computational systems utilize other aspects of the physical world. Reaction-
diffusion systems utilize the chemistry of excitable media [4] (see Sect. 11).
DNA computing, uses the chemistry of DNA interactions [5] [6]. Synthetic
biology builds computational operations inside living cells [100].
It is interesting to note that Toffoli says that “Nothing Makes Sense in
Computing Except in the Light of Evolution” [92]. He argues firstly that a
necessary but not sufficient condition for a computation to have taken place,
is when a novel function is produced from a fixed and finite repertoire of
components (i.e. logic gates, protein molecules). He suggests that a sufficient
condition requires intention. That is to say, we cannot argue that computation
has taken place unless a system has arisen for a higher purpose (this is why
he insists on intention as being a prerequisite for computation). Otherwise,
almost everything is carrying out some form of computation (which is not a
helpful point of view). Thus a Turing machine does not carry out computations
unless it has been programmed to do so, and since natural evolution constructs
organisms whose genes have an increased chance of reproduction [23] (the
higher ‘purpose’) we can regard them as carrying out computations. It is in this
sense that Toffoli points to the fundamental role of evolution in the definition
of a computation as it has provided animals with the ability to have intention.
Conrad criticizes traditional models of computing and he identifies that
they have a common feature: at most very limited context dependency [22].
The logic gates in conventional machines implement formally defined input-
output behaviors that are independent of the overall design of the circuit. Tur-
ing machines read and write symbols on individual tape squares in a manner
that does not depend on the arrangement of symbols on the tape. Whereas
computation in physical systems (particularly biological) are almost always
context dependent.
This brings us to one of the important questions in computation. How can
we program a physical system to perform a particular computation? The usual
answer has been to construct logic gates and from these build a von Neumann
machine (i.e. a digital computer). The mechanism that has been used to devise
a computer program to carry out a particular computation is the familiar top-
down design process, where ultimately the computation is represented using
Boolean operations. According to Conrad this process leads us to pay “The
Price of Programmability” [21], whereby in conventional programming and de-
sign we proceed by excluding many of the processes that may lead to us solving
the problem at hand. Indeed as Zauner notes, programmability is not a strict
requirement for information processing systems since the enviable computing
capabilities of cells and organisms are not implemented by programs. Artificial
neural networks are also not programmable in the normal sense [103].
In this paper we suggest that some form of computer–controlled evolution
ought to be an appropriate methodology for arriving at physical systems that
compute. Since EIM utilizes physical effects to perform computation one can
consider it as a methodology for performing analogue computation. In partic-
ular, it is a general-purpose method for obtaining specific analogue computa-

12 Julian F. Miller et al.
tional devices. In the next section we examine the theoretical underpinnings
of analogue computation. This will help in understanding how EIM relates to
analogue computation.
5 Analogue computation
Prior to the invention of digital computers there existed a variety of analogue
computing machines. Some of these were purely mechanical (e.g. an abacus, a
slide-rule, Charles Babbage’s difference engine, Vannevar Bush’s Differential
Analyser) but later computing machines were built using operational amplifiers
[13,51]. Bush’s differential analyzer was a mechanical analogue computer that
could solve differential equations [18]. Shannon analyzed Bush’s machine and
formulated the mathematical theory behind it [77]. In so doing, he defined
the General Purpose Analogue Computer (GPAC). This is a computer that
operates on continuous variables xi=xi(t) each of which is a function of
an independent variable (often called time) and whose four operations, fiare
defined as:
1. constant: f1=c, where cis a real-valued constant
2. addition: f2(x1, x2) = x1+x2
3. multiplication: f3(a, x1) = ax1
4. integration: f4(x1, x2) = Rt
t0x1(z)dx2(z)
There are restrictions about how these functions can be connected. The
output of each function must either become the input of another function
or be a final output of the computation. Shannon showed that GPACs can
compute any differential algebraic function. However, there has been more
theoretical work extending Shannon’s model to a wider class of computable
functions [29,28].
Rubel defined another mathematical model of a more powerful analogue
computing machine which he called an Extended Analogue Computer (EAC)
[72]. The EAC can produce functions of any finite number of real variables. In
addition, the EAC “produces solutions of a broad class of (initial-and) bound-
ary value problems for partial differential equations”. Rubel uses a larger ar-
ray of “black-box” functions than in the GPAC. His functions included adders,
multipliers, substituters, inverters, differentiators, and some set-theoretic oper-
ators (for more detailed explanations see [60]). The functions must be arranged
in a line in which the outputs from one function are fed into the inputs of the
next function, no two outputs can be connected to the same input, and each
input must be connected to an output. The EAC also has connectivity con-
straints that must be obeyed for its mathematical properties to be provable.
MacLennan gives a mathematical foundation to computers called field com-
puters [50]. These are computers that can “perform (in parallel) transforma-
tions on scalar and vector fields”.
Analogue computation has focused on what kinds of mathematical func-
tions can be provably computed using collections of mathematical primitives.

Evolution-in-materio computation 13
In EIM, the mathematical functions computed by primitive components are
not known explicitly (if at all) and EIM leaves computer-controlled evolution
the job of finding suitable combinations of computational primitives that assist
in solving computational problems. It does not use the traditional methodol-
ogy of building solutions to computational problems by combining relatively
simple components in a principled manner. It works in a very unconventional
design space [54] in which unusual (or even unknown) components are com-
bined and tested and new designs are searched for by evolution.
6 Gordon Pask’s work with Ferrous sulphate
Some might consider that ‘evolution-in-materio’ began in 1958 in the work of
Gordon Pask who worked on experiments to grow neural structures using elec-
trochemical assemblages[19,63, 67]. Gordon Pask’s goal was to create a device
sensitive to either sound or magnetic fields that could perform some form of
signal processing. He likened this to an ear. He realised he needed a system
that was rich in structural possibilities, and chose to use a metal–salt solution.
Using electric currents, thread like metallic structures could self-assemble in an
acidic aqueous metal–salt solution (e.g. ferrous sulphate). Changing the elec-
tric currents can alter the structure of these wires and their positions and the
behavior of the system can be modified through external influence. Pask used
an array of electrodes suspended in a dish containing the metal–salt solution,
and by applying current (either transiently or a slowly changing source) was
able to build iron wires that responded differently to two different frequencies
of sound- 50Hz and 100Hz.
Fig. 2: Pask’s experimental set up for growing dendritic wires in ferrous sul-
phate solution [63]

14 Julian F. Miller et al.
Pask had developed a system whereby he could manually train the wire
formation in such a way that no complete specification had to be given -
a complete paradigm shift from previous engineering techniques which would
have dictated the position and behavior of every component in the system. His
training technique relied on making changes to a set of resistors, and updating
the values with given probabilities - in effect a process of generate-and-test. We
would today recognise this algorithm as some form of hill climbing algorithm.
In a discussion of the epistemological implications of Pask’s work, Cariani
notes that in Pask’s device, the sensory capabilities were emergent, that is to
say they were not predefined [19]. To quote:
Such devices would find their own “relevance criteria”, by adaptively
constructing sensors to gather the information that they needed to solve
a given real world problem. Out of “an infinity of variables” such a
device would come up with a set of variables adequate for a specific task.
Such a device would be the analogue of both the scientist searching for
the right observables for his/her model and the biological evolution of
a new sensory modality.
The issue of deciding which physical variables are most useful and appro-
priate for evolution-in-materio is very difficult. Ideally according to Pask and
Cariani, the physical system should “come up” with appropriate variables.
However, if one requires a computer-controlled automatic system hard deci-
sion have to be taken about what kinds of variables to control. Of course,
inside the computational material, other unknown variables may come into
play. To some extent these can be seen as internal “relevance criteria”. We
will discuss this issue further when we consider advantages and disadvantages
of evolution-in-materio (see Sect 15).
7 Kirchoff-Lukasiewicz machines: Computing with conductive
sheets
Inspired by Rubel’s model of an extended analog computer, Mills constructed
his own version, which he termed, a Kirchhoff-Lukasiewicz Machine (KLM)
[57]. The machines are composed of logical function units connected to a
conductive sheet, typically a conductive polymer sheet. The logical units im-
plement Lukasiewicz Logic - a type of multi-valued logic [59,60]. Figure 3a
shows the component parts of an ethernet networked version of the KLM. The
Lukasiewicz Logic Arrays (LLA) are connected to the conductive polymer. The
LLA bridge areas of the sheet together. The logic units measure the current
at one point, perform a transformation and then apply a current source to the
other end of the bridge.
Computation is performed by applying current sinks and sources to the
conductive polymer and reading the output from the LLAs. Depending on
where on the sheet the signals are placed and the configuration of the LLAs,
different computations can be performed.

Evolution-in-materio computation 15
(a)
(b)
Fig. 3: A labeled schematic of the KLM in 2004 (a) and a photo of a working
KLM with labeled components (b).
Examples of computation so far implemented in this system include robot
control, control of a cyclotron beam [58], models of biological systems (includ-
ing neural networks) [56], radiosity based image rendering and a number of
other applications [60]. Essentially the KLM performs computation by setting
up initial conditions to physically instantiated systems of partial differential
equations. Readout happens after these physical effects have stabilized. Using
this form of analogue computation, a large number of these equations can be
solved in nanoseconds - much faster than on a conventional computer. The
speed of computation is dependent on materials used and the interfacing to
them, but it is expected that silicon implementations could be capable of solv-
ing tens of millions of partial differential equations per second.
The most interesting feature of these devices is the programming method.
It is very difficult to understand the actual processes used by the system
to perform computation. At the moment, programming requires the manual
placement and selection of connections and applied currents. It would be most
interesting to investigate the utility of using an evolutionary algorithm to se-
lect the functions of the LLAs and to define the current sink/sources. It is
interesting to note that although KLMs are clearly using the physical proper-

16 Julian F. Miller et al.
ties of a material to perform computation, the physical state of the material
is not reconfigured.
Mills works suggests that theoretical work on defining types of analogue
computation can usefully inform practical work in evolution-in-materio. It
highlights the possibility that choosing a conductive sheet as configurable ma-
terial has real promise. It remains to be seen whether such “simple” materials
have advantages over more complex materials such as liquid crystal (see Sect
10).
8 From evolution in simulo to evolved physical artefacts
Partly as a matter of completeness we briefly examine work closely related to
evolution-in-materio in which evolution is used to design “buildable ob jects”.
In these systems the “configurable material” is not a real material but either
a virtual entity or a model of a physical object. Despite not directly manipu-
lating a physical object, it is possible for evolutionary algorithms to find novel
solutions to problems that can be subsequently built. Indeed, such systems can
show that evolution can utilize hitherto unknown physical effects in simulation
for problem solving.
Karl Sims created a model of creatures inside a computer [78]. The crea-
tures existed in a virtual world having a simple physics. The creatures were
built out of virtual rectangular blocks with several degrees of freedom. The
blocks and the creatures were invested with an evolved control system. Sims
showed that evolution could arrive at novel designs for creatures that could
achieve higher goals (i.e. running or swimming fast). Evolution was able to
exploit virtual physical laws in innovative and unexpected ways to arrive at
novel solutions.
Funes and Pollack created a simulation of static structures made of Lego
[26,27]. Their evolved simulated novel structures could be physically assembled
afterward. The simulation proved to be reasonably faithful so that behaviour
of the physical structures was similar to that exhibited in simulation.
Hornby and Pollack investigated evolving Lindemayer systems to define
both the neural controllers and the physical assembly of “Tinker-Toy” modular
robots which were capable of movement [40].
Lipson and Pollack also simulated the neural control and physical morphol-
ogy of robots in simulation [47]. However, they carefully defined the simulation
of robot morphology so that it could be printed out using a 3D printer. Af-
ter sufficiently fit robots were evolved and printed, they added motors and
connected up the evolved software neural controllers.
Paul et al. evolved simulations of tensegrity robots which could be subse-
quently built [65]. For a recent review of evolutionary robotics see [14].
Rieffel and Sayles note that few evolved designs are subsequently manufac-
tured into physical objects. One reason for this is that often evolved designs
are descriptive rather than being a detailed plan for how the object might be
constructed. Another is that for highly complex or flexible physical designs,

Evolution-in-materio computation 17
there is too large a discrepancy between the simulated properties of the object
and its actual physical properties when assembled. In such cases one refers to
there being too large a “reality gap”. To bridge this gap, Rieffel and Sayles
recommend using a device called an “EvoFab” within the evolutionary loop.
“EvoFab” is a fully embodied evolutionary fabricator [70].
Bhalla et al. used a rapid prototyping machine to physically realise 3D self-
assembling objects whose self-assembly rules had been evolved in a simulator
[11].
One of the most successful examples of evolved simulated ob jects crossing
the reality gap into the physical world is Linden’s construction of evolved
antennas [45].
Segemented wire antennas were evolved in simulation and subsequently
assembled. Indeed, an evolved design surpassed a state-of-the-art conventional
design and was deployed on a NASA spacecraft in 2006 [49]. Interestingly, to
ensure that the evolved antennas would be relatively insensitive to small errors
in construction, the team of researchers evaluated the simulation fitness on a
number of randomly perturbed designs.
Linden also evolved unusual antennas using reed relays in situ, without
requiring a simulator [46]. He assembled various rigid physical structures us-
ing reed relays and controlled whether the relays were open or closed via an
evolutionary algorithm. He investigated the ability of the antennas to receive
transmitted radio waves. This experiment was in effect a form of evolution-in-
materio in which the configurable material was a structure made of relays and
coils.
Many of these papers illustrate how artificial evolution can exploit simu-
lated physical variables in unexpected and innovative ways. It seems highly
likely that utilizing actual physical systems would furnish evolution with a
much greater range of exploitable effects. In the next section we discuss how
EIM can be easily implemented using programmable arrays of electronic com-
ponents. Indeed, it was work by researchers in a field known as evolvable
hardware that first alerted the evolutionary computation research community
about the rich possibilities afforded by allowing evolution to manipulate hard-
ware directly.
9 Evolution in silico
“Intrinsic evolution” is a term often used by researchers in evolvable hardware
to mean that electronic circuits are configured by evolved genotypes and the
fitness is based on physical measurements of the behaviour of the circuit. The
release of open architecture Field Programmable Gate Arrays (FPGA) partic-
ularly by Xilinx around 1995, greatly assisted researchers to conduct experi-
ments in intrinisic evolution. FPGAs are electronically reconfigurable circuits.
This means that configurations can be downloaded onto an FPGA which de-
fine an electronic circuit [30]. A little later, other intrinsic evolution platforms

18 Julian F. Miller et al.
called Field Programmable Transistor Arrays (FPTAs) were developed [81,43,
95]. These allowed reconfigurable circuits to be built from transistors.
Adrian Thompson started investigating whether it was possible to intrinsi-
cally evolve working electronic circuits using the Xilinx FPGA [88, 85]. He set
himself the task of evolving a digital circuit that could discriminate between
an applied 1kHz or 10kHz signal. He found that computer controlled evolution
of the configuring bit strings could relatively easily solve this problem. How-
ever, when he analyzed the successful circuits he found to his surprise that
they worked by utilizing subtle electrical properties of the silicon.
Working with the same FPGA design, Huelsbergen et al. [41] found simi-
lar odd behaviour while trying to evolve oscillators. They found that evolved
circuits were using transistors in a way that was outside of their normal oper-
ating conditions. Thompson also found that if the designs (as defined by the
configuration bitstring) were moved to another area of the chip they no longer
functioned. They were also very temperature sensitive. He also discovered that
parts of the chip, that according to the configuration bitstring, were not in-
volved in the circuit were in fact contributing to the operation of the evolved
circuit. Despite painstaking analysis and simulation work he was unable to
explain how, or what property was being utilized [89]. This lack of knowledge
of how the system works, of course, prevents humans from designing systems
that are intended to exploit these subtle and complex physical characteristics.
However, it does not prevent exploitation through artificial evolution.
There was concern that such intrinsically evolved circuits would be in-
herently impractical, so in later work Thompson attempted to evolve circuits
under a wide variety of physical conditions in an attempt to obtain designs
that were independent of the physical properties of the FPGAs [87,90]. He
was able to achieve circuits that were robust to most but not all environmen-
tal conditions. Stoica et al. advocated a strategy called “mixtrinsic evolution”
in which fitness is evaluated both in hardware and in simulation and found
that this increased the likelihood of obtaining portable evolved designs [82].
Through constraints on types of allowed configurations and specially designed
evolutionary operators, Trefzer was able to evolve circuits on FPTAs that
were portable and whose simulated behaviour accorded with their physical
behaviour [96].
Stoica et al. also examined the ability of evolutionary algorithms to recon-
figure FPTAs to recover particular functions when the FPTA chip had been
damaged by high-energy electrons [80]. Radiation damaged chips lose their
functionality. The evolutionary algorithm used controlled the state of about
1,500 switches that determined the circuits configurations on the FTPA pro-
grammable device. They found that provided the level of damage was not too
great, it was possible for evolution to find new circuit configurations that re-
covered the original function. Interestingly, often the evolutionary algorithm
found a working circuit configuration that utilized the damaged parts of the
FPTA.
Evolving circuits with an FPGA has limitations as the types of compo-
nents used are predefined by the manufacturer. Another drawback is that the

Evolution-in-materio computation 19
elements of the evolved circuit are not fully testable or easily inspectable. In
response to this Paul Layzell created his own platform on which to carry out
experiments in intrinsic evolution. He called his circuit an evolvable mother-
board (EM) [44]. Layzell performed several experiments with this board to
demonstrate that it was a suitable platform for evolution. In the first exper-
iment he evolved a digital inverter (a NOT gate) using two transistors. The
evolved design was unconventional, and was found to contain an interesting
and unexpected feature - evolution had made no use of the 0V line on the EM.
This should have meant that the circuit would not work - however evolution
had used an oscilloscope connected for observing the results! The path to 0V
required the 10MΩ impedance of the oscilloscopes test lead. Removing the
oscilloscope from the circuit stopped the inverter from operating. In another
experiment he evolved an oscillator. He found that substituting transistors
in evolved functioning solutions with nominally identical ones produced large
changes (as much as 30%) in the output frequency - evolution was depen-
dent on the specific electrical characteristics of the components. Some of the
evolved circuits exploited features of the environment. The first observation
was that some oscillators failed to work if a soldering iron, several meters from
the EM, was disconnected from the mains. This was regardless of whether
the iron was on or off. The other observation was that some oscillators were
‘cheating’ and had evolved simple radio receivers that picked up oscillations at
the correct frequency [12]. Evolution had used the copper tracks and the other
components in the circuit to form aerials, and the signals were connected to
the output of the device.
10 Evolved computation in Liquid Crystal
In 2002, Miller and Downing discussed the concept of evolution-in-materio and
suggested that liquid crystal might be a suitable material for attempting to
evolve computation in materials [53]. They also discussed many other materials
whose properties can be affected reversibly via physical signals.
Utilizing the evolvable motherboard concept of Layzell, Harding constructed
a liquid crystal analogue processor (LCAP) that utilizes the physical proper-
ties of liquid crystal for computation [32]. The experimental setup used by
Harding was similar in concept to that used by Thompson [88,85]. This is
shown in Fig. 4a(a). A photograph of the LCAP is given in Fig. 4b(b).
Harding used four cross-switch matrix devices to dynamically configure
circuits connecting to the liquid crystal. The switches are used to wire the 64
connections on the LCD to one of 8 external connections. The external connec-
tions are: input voltages, grounding, signals and connections to measurement
devices. Each of the external connectors can be wired to any of the connec-
tions on the LCD. The external connections of the LCAP are connected to the
I/O card of a PC. One connection was assigned for the incident signal, one for
measurement and the other for fixed voltages. The value of the fixed voltages

20 Julian F. Miller et al.
(a)
(b)
Fig. 4: Liquid Crystal Analogue Processor. (a) Computer-controlled evolution-
ary loop (b) Photo of device.
is determined by the evolutionary algorithm, but is constant throughout each
evaluation. A schematic of the LCAP is given in Fig. 5.
Harding has shown that a number of different computational problems can
be evolved using the LCAP:

Evolution-in-materio computation 21
Liquid Crystal Display
8x16 Analog Switch Array
8 External Connectors
LCD contacts,
32 per side
- 64 in total.
Fig. 5: Schematic of Liquid Crystal Analogue Processor. Part of the genotype
defined on the computer decides which electrodes on a LC display will be con-
nected to one of eight contacts on the printed circuit board. Certain contacts
are designated to receive square wave signals, others receive fixed analogue
voltages and another is connected to ground. The other part of the genotype
decides the magnitude of the voltages to apply.
–Tone discriminator. A device was evolved in liquid crystal that could dif-
ferentiate many different frequencies of square wave [32].
–Logic gates. A variety of two input logic gates were evolved, showing that
liquid crystal could behave in a digital fashion. This indicates that liquid
crystal is capable of universal computation [36].
–Robot controller. An obstacle avoidance system for a simple exploratory
robot was evolved. The results were highly competitive, with other work
on evolved robot controllers as it took relatively few evaluations to evolve
a working robot controller [33].
It turned out to be relatively easy to evolve the configuration of liquid
crystal to solve tasks i.e. only 40 generations of a modest population of config-
urations are required to evolve a very good frequency discriminator, compared
to the thousands of generations required to evolve a similar circuit on an FPGA
[88,85].

22 Julian F. Miller et al.
11 Reaction-diffusion computers
Reaction diffusion systems are mathematical models which explain how spa-
tially distributed concentrations of chemicals change under the influence of two
processes: local chemical reactions and diffusion. Adamatzky pioneered the use
of reaction-diffusion systems for computation. He describes reaction-diffusion
computers as chemical systems which can process information using interact-
ing growing patterns, of excitable and diffusive chemicals [2]. Data input and
output is encoded as concentration profiles of chemical reagents. When differ-
ent chemical wave fronts interact computation is performed. Such computers
are massively parallel since micro–volumes update their states simultaneously,
and molecules diffuse and react in parallel. These microvolumes change their
state based on local interactions. Inputs and outputs are usually performed op-
tically by supplying illumination masks and for output using imaging systems.
Reaction diffusion computational devices have already been shown to solve a
range of computational problems, most notably large scale Voronoi diagram
construction (which is NP complete). Computationally universal logic gates
have been devised. Reaction-diffusion systems can also be controlled via elec-
tric fields. Hybrid wetware conventional hardware (webcam and conventional
electronics) have been used in “intelligent” robot control [1,4]
Evolutionary algorithms have been used to control a light-sensitive Belousov-
Zhabotinsky (BZ) reaction so that it implements single two–input logic gates
(AND, NAND and XOR) [93]. This was achieved by evolving the rules of a
heterogeneous cellular automaton to control the light intensity projected onto
the surface of a light-sensitive catalyst–infused gel. Also Toth et al. were able
to control chemical wave fragments in light-sensitive BZ reactions using evo-
lutionary algorithms to implement collision-based two-input logic gates (AND
and NAND) [94]. A learning classifier system XCS has also been used to control
chemical-wave fragments in light-sensitive BZ reactions [16].
12 Nuclear magnetic resonance and computation
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei
in a magnetic field absorb and then re-emit electromagnetic radiation. Rosello
et al. showed how it was possible to implement two-input logic gates by us-
ing a variety of radio-frequency pulse parameters. These parameters include
pulse amplitude, duration, frequency and phase [71]. In addition, pulses can
be applied in sequence.
To implement logic gates one has to decide how to represent binary inputs
and how to read the output. One methodology uses pulse sequences which
are called pulsed gradient spin echo (PGSE) sequences. In this, one input is
decided by whether a starting pulse (a 90 degree pulse) is supplied with a
characteristic frequency (resonance) or not. On-resonance represents a 0 and
off-resonance represents a 1. The delay before the radio-frequency response of
the system is read (data acquisition delay) determines the state of the second

Evolution-in-materio computation 23
input. If data acquisition (DA) starts immediately after an on-resonance pulse
the second input is considered to be 0. If DA starts a given time after the
on-resonance pulse, the second input is interpreted as a 1. If the start pulse
is off-resonance, and the DA delay is 0, the second input is defined to be 0.
Finally, if the start pulse is off-resonance and the DA delay is non-zero, the
second input is defined to be 1. One method of deciding whether an output is
one or zero is to examine the integral of the spectral intensity (in the frequency
domain). A zero total integral is interpreted as an output bit value of 0, a non-
zero total integral as 1.
Bechmann et al. pointed out that the underlying continuous spin dynamics
can also provide a basis for what they described as “continuous logic opera-
tions” [8]. This means that the inputs and outputs are no longer restricted to
be the discrete values 0 or 1, but can be any value between 0 and 1. They
defined some simple continuous gates (referred to as sin/sin or sin/sinc) and
using a form of genetic programming called Cartesian Genetic Programming
[55] evolved circuits made of these gates that could function as digital (by
rounding) even if the inputs have considerable errors (i.e. are real values be-
twen 0 and 1).
13 Evolution in vitro: optimizing amphiphilic vesicles using genetic
algorithms
Thies et al. [84] investigated how a genetic algorithm can optimize, or at least
improve, the functionality of an amphiphilic chemical system. Although the
aim of their work was not focused on computation it is still interesting to con-
sider as it involves many of the issues that are faced in evolving computation
using materials.
Amphiphilic chemicals form vesicles in an appropriate solvent. The genetic
algorithm is applied to a population of chemical systems realized in the labora-
tory. The genetic representation only allowed 5 from 16 amphiphilic chemicals
to be chosen. After a time-consuming process of preparation the amphiphiles
were mixed in a sucrose solution. Three identical mixtures were prepared for
each genotype. The turbidity (or cloudiness) of each of the three identical
recipes was measured. Turbidity was chosen merely because it is straightfor-
ward to measure, however it correlates well with the size and abundance of
vesicles. The fitness of a genotype was defined as the mean turbity minus its
standard deviation over the three mixtures. Due to the extreme time consum-
ing nature of the process, only 5 generations using a population of 30 was used.
In the evolutionary run they generated a total of 180 recipes which equates to
1.16% of the search space (15,504 possible recipes). It was possible to analyse
which recipes acheived the highest fitness and learn about interesting interac-
tions between the chemicals. This is an example of how evolution-in-materio
has the potential to generate new science.

24 Julian F. Miller et al.
14 Materials for evolution-in-materio
It is likely that a search algorithm will to need to examine many thousands
of configurations of materials to arrive at set that allows the material to solve
a useful computational problem. This implies that ideal materials must be
able to be configured in fractions of a second. In addition, it would be helpful
to be able to apply test signals and read off responses rapidly. This suggests
systems that respond rapidly to electrical signals are most favourable. Miller
and Downing discussed a number of potential materials that look promising for
evolution-in-materio [53]. These are: liquid crystal, nanoparticle suspensions,
molecular films, conducting polymer composites, voltage-controlled colloids,
electrorheological fluids and irradiated or otherwise damaged semiconductors.
The latter is suggested because it may have more exploitable physics than
undamaged silicon. Oltean suggest that electrochromic materials could be used
[62].
Rietman showed that it was in principle possible to use a genetic algorithm
to program magnetic quantum dots for use in pattern recognition and evolve
crystalline programmable resistor arrays for computation [37]. Other promis-
ing systems include: Biological or chemical systems that can be manipulated
electronically using microfluidics [83] or microbial consortia manipulation us-
ing dielectrophoresis [98].
In European FP7-ICT funded NASCENCE project a group of researchers
are investigating evolution-in-materio using microlectrode arrays [15]. In this
project a variety of materials are being actively investigated for their useful-
ness in an evolution-in-materio context. Materials such as carbon nanotubes
and metallic nanoparticles, can be placed in small chambers surrounded by
many tiny electrodes. Using an evolutionary algorithm and computer con-
trol, voltages can be applied to electrodes to configure materials to carry out
computational tasks. With this device it will be possible to investigate many
materials to see if they can be exploited for computation.
It is worth recalling that in Mill’s KLM no material is fundamentally
changed during configuration. In other words the material is passive, the con-
figuration voltages or currents just determine the initial conditions for sets
of physically instantiated partial differential equations. This suggests that it
may not be necessary to use complex materials in evolution-in-materio. Fur-
ther work is required to establish the most suitable material substrates for
various kinds of computational problems.
15 Fundamental aspects of evolution-in-materio
We have examined many systems in which computer controlled evolution could
be used to configure physical systems so that useful computation could be
obtained. Here we discuss possible challenges, advantages and disadvantages
of this approach.
Possible advantages are listed below:

Evolution-in-materio computation 25
1. A computer model of the physical system is not required;
2. Physical variables can be utilized by evolution without knowing that such
variables exist in advance;
3. The physical system already exists and does not require assembly after
evolution has finished;
4. Allowing evolution to utilize physical effects may increase evolvability;
5. It is possible that hitherto unknown computational devices could be dis-
covered;
6. Computer controlled evolution can explore potential solutions that humans
would find inconceivable.
7. The amount of computation a small piece of material can do may be enor-
mous.
Possible disadvantages include:
1. The time taken to apply a configuration of physical signals may be pro-
hibitive;
2. The boundaries of what constitutes the evolved system may be unclear and
poorly defined;
3. It is not always clear what physical variables are most appropriate;
4. Applying test signals (over which fitness may be evaluated) may change
the intrinsic properties of the system;
5. The system may exhibit weak reproducibility, in that, under identical con-
ditions at different times it may exhibit different behaviour;
6. Evolved physical devices are not universal in a Turing sense. Each problem
requires a unique configuration of a physical device to be found.
The advantage 1 may be particularly useful in situations where either sim-
ulators do not currently exist or it would be prohibitively expensive to build
and run simulations. However, there are some systems that can be simulated
faithfully where the computational cost is not prohibitive. An example of this
is Linden and Altshuler’s work on evolving antennas [45].
Advantage 2 is one of the principal advantages of manipulating matter via
an evolutionary algorithm. By merely requiring that a piece of matter perform
a particular computation could allow a host of physical processes to be utilized
in novel ways. In a sense this is what natural evolution has done with protein
chemistry. Evolution-in-materio does not pay “the price of programmability”
as the computation is not being performed in the Turing sense.
Advantage 3 is self-evident and is why we argue that evolution-in-materio
sits at at level of embodiment equal to 2.5 according to Eiben’s scheme. How-
ever, although 3 is an advantage, it has the potential disadvantage that it is
not clear what the boundaries of the physical system are. More work needs to
be done in evolution-in-materio research to study isolation mechanisms. How
can we exploit physical effects in an isolated system? It is well known how
artificial evolution is able to exploit strange unanticipated quirks. Interest-
ingly, this problem also exists in quantum computing, in that the interesting
computation happens in very fragile entangled states. To counter Conrad’s

26 Julian F. Miller et al.
phrase one could say that physical computation will have to pay the “price of
physicality”!
Potential advantage 4 is intriguing. Harding et al. found that it was rela-
tively easy to evolve a tone discriminator in liquid crystal, much easier than
Thompson found it to be in silicon. Conceptually, we can understand this since
most physical systems are likely to be endowed with many exploitable proper-
ties. We refer to this as richness. Silicon based electronic circuits have had the
physics constrained as much as possible to implement Boolean logic and thus
allow Turing computation. One way of possibly testing the relationship with
richness and evolvability would be to attempt to evolve solutions to computa-
tional problems on a variety of FPGAs (say) with varying degrees of damage
(perhaps by irradiating them). Experiments with radiation damaged FPTAs
showed that evolutionary algorithms could make use of damaged parts of the
chip (See Sect. 9). It remains to be seen if such damage actually helps solve
certain computational problems. Richness and Turing computation appear to
be in opposition to one another as Turing computation is based on perfect
symbolic operations in which physical effects don’t even exist.
Potential advantage 5 is the raison d’etre of evolution-in-materio. Pask,
Thompson, Harding and Linden have shown the way. This is why this area
of research is exciting, new physical principles could be discovered that allow
us to develop new technology. Many computational problems are difficult or
intractable to understand. This is a barrier to technological development. The
closely related potential advantage 6 suggests that computer-controlled evolu-
tion may allow us to develop solutions to problems that are inconceivable to
human beings whether they use new physical principles or not. Potential ad-
vantage 7 raises many interesting questions. It may be possible to evolve very
sophisticated computational processors using a very tiny sample of material.
In the NASCENCE project, tiny electrode arrays are being used. How small
can we go? This is an intriguing question. It is worth noting that Seth Lloyd
has calculated the potential amount of computation possible in matter [48].
He calculated that 1Kg of matter should be able to carry out about 5.51050
operations per second and store 1031 bits.
Potential disadvantage 1 concerns the time taken to physically configure
a material. In many cases, this is a very real problem. Thies et al. described
how it took hours to prepare their mixtures of chemicals so that a fitness
measurement was possible [84]. Likewise, at present it takes a long time to
prepare reaction-diffusion systems (see Sect.11). However in other forms of
evolution-in-materio and physical computing systems this is less of a problem
(e.g. silicon, liquid crystal and conductive sheets). However, from a program-
ming point of view, it can be considered to take a long time for evolution to
configure a system to perform the desired computation. Though this is true,
it should be noted that writing conventional computer programs also takes a
long time.
Disadvantage 2 is concerned with separability. How can we separate the
computation allegedly being carried out by the target device, and that ac-
tually done by the material being used. We have already noted examples of

Evolution-in-materio computation 27
non-separability in Sect. 9. An evolved device may not be useful if it highly
sensitive to its environment in unpredictable ways, and it will not always be
clear what environmental effects the system is using. To minimise these risks,
an evolved system will need to assessed under a range of different environ-
mental conditions. Also as mentioned above methods of isolation need to be
investigated.
Disadvantage 3 is a potentially serious problem. Deciding on appropriate
physical variables to configure a device is not obvious and normally requires
a great deal of insight from a domain expert. To some extent, one should be
prepared to investigate a number of ways of configuring materials. Thompson
and Harding both used square wave signals as inputs. They both measured the
percentage time an output was high as an output signal (i.e. they used digital
outputs evaluated over time). Deciding how an input should be applied and
an output measured and indeed, what is constitutes an appropriate and useful
evolvable physical configuration is a difficult issue. Ideally, we want evolution
to construct its own input and output mechanism as in the case of Pask’s
experiments discussed in Sect. 6. It might be considered that artificial curiosity
algorithms could have a role here [74]. However, although curiosity algorithms
can build an internal model of behaviour and look for learnable but unknown
regularities they can not introduce entirely new physical variables into an
existing model. As we observed in 5 the point of evolution-in-materio is that by
allowing computer-controlled evolution to apply, read and manipulate physical
variables it may be able to exploit possibly unknown modalities of operation. In
a very thought-provoking analysis of the epistemological implications of Pask’s
work Cariani emphasized the importance of techniques that find their own
“relevance criteria” [19]. Devising ways of doing computer-controlled evolution
so that useful physical variables can be discovered, measured and used for
rewarding good partial solutions is a very difficult problem that requires much
further research.
Disadvantage 4 was evident in the liquid crystal analogue processor of
Harding [31,34]. When the liquid crystal display is observed while solving a
problem it is seen that some regions of the liquid display go dark indicating
that the local molecular direction has been changed. This means that the con-
figuration of the liquid crystal is changing through the action of test signals.
We normally think of such a thing as undesirable. For example, if this hap-
pened with conventional computer programs it would mean that the program
itself could change in response to test inputs. Thus its behaviour would be
dependent on its history. However, viewed from the point of view of a state-
machines, this is less worrying. A remedy for this might be merely that we
need a reset condition, in which we can place a material in approximately the
same initial state. A more pragmatic view would be to say that the fitness
function automatically measures the stability of computation over the period
of the evaluation. Changes made by the incident signals can be considered part
of the genotype-phenotype mapping. Solutions that cannot cope with their ini-
tial configurations being altered will achieve a low score. However, the fitness
function cannot measure the behaviour beyond the end of the evaluation time.

28 Julian F. Miller et al.
Therein lies the difficulty, in evolution-in-materio long term stability cannot
be guaranteed.
Disadvantage 5 concerns reproducibility. In the case of liquid crystal, liquid
crystal molecules are unlikely go back to exactly to a previous state. Stoica
et al. also observed that the behaviour of evolved circuits on FPTAs could be
dependent of previous configurations[82]. This implies that identical configu-
rations will not produce exactly the same behaviour. This is not necessarily
a fundamental problem for evolution provided there is a strong correlation
between genotype and phenotype. However, if evolved devices are to be useful
in a conventional sense one needs to be sure that previously evolved devices
will function in the same way as they did when originally evolved. In Mill’s
conductive sheets, physical configurations relax back extremely quickly as the
substrate is conductive so current dissipates quickly, however there could still
be problem if heating occurs as this would change the properties. It is worth
noting that natural evolution does not exhibit this exact reproducibility ei-
ther. Organisms are always different from one another (even if they have the
same genome). It is likely that evolved devices will only approximately have
the same behaviour.
Disadvantage 6 concerns the potential disadvantages that all analogue com-
puters have. Digital computers are based on the notions of a universal Turing
machine. In practical terms this means that digital computers can be pro-
grammed to solve many types of computational problems. The data stored
in memory changes but the physical architecture does not change. Programs
written in high-level languages can be compiled into low level instructions and
then executed on the same machine. At present, we are arguing that computer
controlled evolution is the method for programming a material. However, us-
ing a search process to find a program may not scale to large computational
problems. Even if this were true, it may be possible that we can evolve useful
functional primitives in materials, which we can later extract and build into
analogue “instructions” that more conventional modes of programming can
utilize.
16 Conclusions and future outlook
We have discussed attempts to use evolution to manipulate physical systems,
particularly but not exclusively, attempts to evolve systems so that they per-
form useful computation. In our view, computer controlled evolution gives us
the possibility to return to analogue computing and build new kinds of compu-
tational devices that in the heyday of analogue computing were impossible to
imagine. One of the difficulties of analogue computers was that they had to be
setup by experts who could create analogues of specific systems in convenient
physical devices. Using a search process running on a modern digital computer
gives us a new way to “program” a physical device. It also gives us a method-
ology for the discovery of new computational devices that use physical effects
for computation in ways that human ingenuity has thus far failed to invent.

Evolution-in-materio computation 29
The field of evolution-in-materio is still a very young and small community
and it is hoped that this paper will serve not only as an introduction to the
field but it will encourage more researchers to contribute to this exciting area
of research.
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