Natural computing,G.Rozenberg, T.Back, J.Kok, Editors, Handbook of Natural Computing, Springer Verlag, 2012A.Brabazon, M.O'Neill, S.McGarraghy
Natural Computing Algorithms
Springer Verlag, 2015 also called natural computation, is a terminology introduced to encompass three classes of methods: 1) those that take inspiration from nature for the development of novel problem-solving techniques; 2) those that are based on the use of computers to synthesize natural phenomena; and 3) those that employ natural materials (e.g., molecules) to compute. The main fields of research that compose these three branches are artificial neural networks,

evolutionary algorithms In computational intelligence (CI), an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduct ...

, swarm intelligence,

artificial immune systems In artificial intelligence, artificial immune systems (AIS) are a class of computationally intelligent, rule-based machine learning systems inspired by the principles and processes of the vertebrate immune system. The algorithms are typically modele ...

, fractal geometry,

artificial life Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry ...

DNA computing DNA computing is an emerging branch of unconventional computing which uses DNA, biochemistry, and molecular biology hardware, instead of the traditional electronic computing. Research and development in this area concerns theory, experiments, a ...

, and quantum computing, among others. Computational paradigms studied by natural computing are abstracted from natural phenomena as diverse as

self-replication Self-replication is any behavior of a dynamical system that yields construction of an identical or similar copy of itself. Biological cells, given suitable environments, reproduce by cell division. During cell division, DNA is replicated and c ...

, the functioning of the

brain A brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as vision. It is the most complex organ in a ve ...

Darwinian evolution Darwinism is a theory of biological evolution developed by the English naturalist Charles Darwin (1809–1882) and others, stating that all species of organisms arise and develop through the natural selection of small, inherited variations that ...

group behavior Group dynamics is a system of behaviors and psychological processes occurring within a social group (''intra''group dynamics), or between social groups ( ''inter''group dynamics). The study of group dynamics can be useful in understanding decision- ...

, the

immune system The immune system is a network of biological processes that protects an organism from diseases. It detects and responds to a wide variety of pathogens, from viruses to parasitic worms, as well as cancer cells and objects such as wood splint ...

, the defining properties of life forms, cell membranes, and

morphogenesis Morphogenesis (from the Greek ''morphê'' shape and ''genesis'' creation, literally "the generation of form") is the biological process that causes a cell, tissue or organism to develop its shape. It is one of three fundamental aspects of deve ...

. Besides traditional

electronic hardware Electronic hardware consists of interconnected electronic components which perform analog or logic operations on received and locally stored information to produce as output or store resulting new information or to provide control for output act ...

, these computational paradigms can be implemented on alternative physical media such as biomolecules (DNA, RNA), or trapped-ion quantum computing devices. Dually, one can view processes occurring in nature as information processing. Such processes include

self-assembly Self-assembly is a process in which a disordered system of pre-existing components forms an organized structure or pattern as a consequence of specific, local interactions among the components themselves, without external direction. When the ...

, developmental processes,

gene regulation Regulation of gene expression, or gene regulation, includes a wide range of mechanisms that are used by cells to increase or decrease the production of specific gene products (protein or RNA). Sophisticated programs of gene expression are wi ...

networks,

protein–protein interaction Protein–protein interactions (PPIs) are physical contacts of high specificity established between two or more protein molecules as a result of biochemical events steered by interactions that include electrostatic forces, hydrogen bonding and th ...

networks, biological transport (

active transport In cellular biology, ''active transport'' is the movement of molecules or ions across a cell membrane from a region of lower concentration to a region of higher concentration—against the concentration gradient. Active transport requires cellul ...

passive transport Passive transport is a type of membrane transport that does not require energy to move substances across cell membranes. Instead of using cellular energy, like active transport, passive transport relies on the second law of thermodynamics to dri ...

) networks, and gene assembly in

unicellular organism A unicellular organism, also known as a single-celled organism, is an organism that consists of a single cell, unlike a multicellular organism that consists of multiple cells. Organisms fall into two general categories: prokaryotic organisms a ...

s. Efforts to understand biological systems also include engineering of semi-synthetic organisms, and understanding the universe itself from the point of view of information processing. Indeed, the idea was even advanced that information is more fundamental than matter or energy. The Zuse-Fredkin thesis, dating back to the 1960s, states that the entire universe is a huge

cellular automaton A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tesse ...

which continuously updates its rules.Fredkin, F. Digital mechanics: An informational process based on reversible universal CA. Physica D 45 (1990) 254-270Zuse, K. Rechnender Raum. Elektronische Datenverarbeitung 8 (1967) 336-344 Recently it has been suggested that the whole universe is a quantum computer that computes its own behaviour.Lloyd, S
Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos
Knopf, 2006 The universe/nature as computational mechanism is addressed by,Zenil, H
A Computable Universe: Understanding and Exploring Nature as Computation
World Scientific Publishing Company, 2012 exploring nature with help the ideas of computability, and Dodig-Crnkovic, G. and Giovagnoli, R
COMPUTING NATURE
Springer, 2013 studying natural processes as computations (information processing).

Nature-inspired models of computation

The most established "classical" nature-inspired models of computation are cellular automata, neural computation, and evolutionary computation. More recent computational systems abstracted from natural processes include swarm intelligence, artificial immune systems, membrane computing, and amorphous computing. Detailed reviews can be found in many books .Olarius S., Zomaya A. Y.
Handbook of Bioinspired Algorithms and Applications
Chapman & Hall/CRC, 2005.de Castro, L. N., Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications, CRC Press, 2006.

Cellular automata

A cellular automaton is a

dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...

consisting of an array of cells. Space and time are discrete and each of the cells can be in a finite number of states. The cellular automaton updates the states of its cells synchronously according to the transition rules given ''a priori''. The next state of a cell is computed by a transition rule and it depends only on its current state and the states of its neighbors.

Conway's Game of Life The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no furthe ...

is one of the best-known examples of cellular automata, shown to be computationally universal. Cellular automata have been applied to modelling a variety of phenomena such as communication, growth, reproduction, competition, evolution and other physical and biological processes.

Neural computation

Neural computation is the field of research that emerged from the comparison between computing machines and the human

nervous system In biology, the nervous system is the highly complex part of an animal that coordinates its actions and sensory information by transmitting signals to and from different parts of its body. The nervous system detects environmental changes ...

.von Neumann, J
The Computer and the Brain
Yale University Press, 1958 This field aims both to understand how the

living organisms In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells (cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and fun ...

works ( brain theory or

computational neuroscience Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, computer simulations, theoretical analysis and abstractions of the brain to u ...

), and to design efficient algorithms based on the principles of how the human brain processes information (Artificial Neural Networks, ANN Arbib, M., editor. The Handbook of Brain Theory and Neural Networks. MIT Press, 2003.). An

artificial neural network Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected unit ...

is a network of

artificial neurons An artificial neuron is a mathematical function conceived as a model of biological neurons, a neural network. Artificial neurons are elementary units in an artificial neural network. The artificial neuron receives one or more inputs (representing e ...

.Rojas, R. Neural Networks: A Systematic Introduction. Springer, 1996 An artificial neuron ''A'' is equipped with a function

f_A

, receives ''n''

real-valued In mathematics, value may refer to several, strongly related notions. In general, a mathematical value may be any definite mathematical object. In elementary mathematics, this is most often a number – for example, a real number such as or an i ...

inputs

x_1, x_2, \ldots, x_n

with respective weights

w_1, w_2, \ldots, w_n

, and it outputs

f_A(w_1x_1 + w_2x_2 + \ldots + w_nx_n)

. Some neurons are selected to be the output neurons, and the network function is the vectorial function that associates to the ''n'' input values, the outputs of the ''m'' selected output neurons. Note that different choices of weights produce different network functions for the same inputs. Back-propagation is a supervised learning method by which the weights of the connections in the network are repeatedly adjusted so as to minimize the difference between the vector of actual outputs and that of desired outputs. Learning algorithms based on backwards propagation of errors can be used to find optimal weights for given topology of the network and input-output pairs.

Evolutionary computation

Evolutionary computationBäck, T., Fogel, D., Michalewicz, Z., editors. Handbook of Evolutionary Computation. IOP Publishing, U.K., 1997 is a computational paradigm inspired by

. An artificial evolutionary system is a computational system based on the notion of simulated evolution. It comprises a constant- or variable-size population of individuals, a fitness criterion, and genetically inspired operators that produce the next

generation A generation refers to all of the people born and living at about the same time, regarded collectively. It can also be described as, "the average period, generally considered to be about 20–⁠30 years, during which children are born and gr ...

from the current one. The initial population is typically generated randomly or heuristically, and typical operators are

mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA replication, DNA or viral repl ...

and recombination. At each step, the individuals are evaluated according to the given fitness function ( survival of the fittest). The next generation is obtained from selected individuals (parents) by using genetically inspired operators. The choice of parents can be guided by a selection operator which reflects the biological principle of

mate selection Mate choice is one of the primary mechanisms under which evolution can occur. It is characterized by a "selective response by animals to particular stimuli" which can be observed as behavior.Bateson, Paul Patrick Gordon. "Mate Choice." Mate Choic ...

. This process of simulated

evolution Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...

eventually converges towards a nearly optimal population of individuals, from the point of view of the fitness function. The study of evolutionary systems has historically evolved along three main branches:

Evolution strategies In computer science, an evolution strategy (ES) is an optimization technique based on ideas of evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies. History The 'evolution strategy' optimiza ...

provide a solution to parameter optimization problems for real-valued as well as discrete and mixed types of parameters.

Evolutionary programming Evolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve. It was fir ...

originally aimed at creating optimal "intelligent agents" modelled, e.g., as finite state machines.

Genetic algorithms In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to gene ...

Koza, J
Genetic Programming: On the Programming of Computers by Means of Natural Selection
MIT Press, 1992 applied the idea of evolutionary computation to the problem of finding a (nearly-)optimal solution to a given problem. Genetic algorithms initially consisted of an input population of individuals encoded as fixed-length bit strings, the genetic operators mutation (bit flips) and recombination (combination of a prefix of a parent with the suffix of the other), and a problem-dependent fitness function. Genetic algorithms have been used to optimize computer programs, called

genetic programming In artificial intelligence, genetic programming (GP) is a technique of evolving programs, starting from a population of unfit (usually random) programs, fit for a particular task by applying operations analogous to natural genetic processes to t ...

, and today they are also applied to real-valued parameter optimization problems as well as to many types of combinatorial tasks.

Estimation of Distribution Algorithm ''Estimation of distribution algorithms'' (EDAs), sometimes called ''probabilistic model-building genetic algorithms'' (PMBGAs), are stochastic optimization methods that guide the search for the optimum by building and sampling explicit probabilis ...

(EDA), on the other hand, are evolutionary algorithms that substitute traditional reproduction operators by model-guided ones. Such models are learned from the population by employing machine learning techniques and represented as Probabilistic Graphical Models, from which new solutions can be sampled or generated from guided-crossover.

Swarm intelligence

Swarm intelligence,Engelbrecht, A. Fundamentals of Computational Swarm Intelligence. Wiley and Sons, 2005. sometimes referred to as collective intelligence, is defined as the problem solving behavior that emerges from the interaction of individual agents (e.g.,

bacteria Bacteria (; singular: bacterium) are ubiquitous, mostly free-living organisms often consisting of one Cell (biology), biological cell. They constitute a large domain (biology), domain of prokaryotic microorganisms. Typically a few micrometr ...

ants Ants are Eusociality, eusocial insects of the Family (biology), family Formicidae and, along with the related wasps and bees, belong to the Taxonomy (biology), order Hymenoptera. Ants evolved from Vespoidea, vespoid wasp ancestors in the Creta ...

termites Termites are small insects that live in colonies and have distinct castes (eusocial) and feed on wood or other dead plant matter. Termites comprise the infraorder Isoptera, or alternatively the epifamily Termitoidae, within the order Blattod ...

, bees,

spiders Spiders (order Araneae) are air-breathing arthropods that have eight legs, chelicerae with fangs generally able to inject venom, and spinnerets that extrude silk. They are the largest order of arachnids and rank seventh in total species di ...

fish Fish are aquatic, craniate, gill-bearing animals that lack limbs with digits. Included in this definition are the living hagfish, lampreys, and cartilaginous and bony fish as well as various extinct related groups. Approximately 95% of ...

, birds) which communicate with other agents by acting on their local environments. Particle swarm optimization applies this idea to the problem of finding an optimal solution to a given problem by a search through a (multi-dimensional) solution space. The initial set-up is a swarm of ''particles'', each representing a possible solution to the problem. Each particle has its own

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...

which depends on its previous velocity (the inertia component), the tendency towards the past personal best position (the nostalgia component), and its tendency towards a global neighborhood optimum or local neighborhood optimum (the social component). Particles thus move through a multidimensional space and eventually converge towards a point between the global best and their personal best. Particle swarm optimization algorithms have been applied to various optimization problems, and to

unsupervised learning Unsupervised learning is a type of algorithm that learns patterns from untagged data. The hope is that through mimicry, which is an important mode of learning in people, the machine is forced to build a concise representation of its world and t ...

, game learning, and

scheduling A schedule or a timetable, as a basic time-management tool, consists of a list of times at which possible tasks, events, or actions are intended to take place, or of a sequence of events in the chronological order in which such things are ...

applications. In the same vein, ant algorithms model the foraging behaviour of ant colonies. To find the best path between the nest and a source of food, ants rely on indirect communication by laying a

pheromone A pheromone () is a secreted or excreted chemical factor that triggers a social response in members of the same species. Pheromones are chemicals capable of acting like hormones outside the body of the secreting individual, to affect the behavio ...

trail on the way back to the nest if they found food, respectively following the concentration of pheromones if they are looking for food. Ant algorithms have been successfully applied to a variety of combinatorial optimization problems over discrete search spaces.

Artificial immune systems

Artificial immune systems (a.k.a. immunological computation or immunocomputing) are computational systems inspired by the natural immune systems of biological organisms. Viewed as an information processing system, the natural immune system of organisms performs many complex tasks in

parallel Parallel is a geometric term of location which may refer to: Computing * Parallel algorithm * Parallel computing * Parallel metaheuristic * Parallel (software), a UNIX utility for running programs in parallel * Parallel Sysplex, a cluster of ...

and

distributed computing A distributed system is a system whose components are located on different networked computers, which communicate and coordinate their actions by passing messages to one another from any system. Distributed computing is a field of computer sci ...

fashion.Dasgupta, D. editor. Artificial Immune Systems and Their Applications. Springer, 1998 These include distinguishing between self and nonself,de Castro, L., Timmis, J
Artificial Immune Systems: A New Computational Intelligence Approach
Springer, 2002. neutralization of nonself

pathogens In biology, a pathogen ( el, πάθος, "suffering", "passion" and , "producer of") in the oldest and broadest sense, is any organism or agent that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a ger ...

(

viruses A virus is a submicroscopic infectious agent that replicates only inside the living cells of an organism. Viruses infect all life forms, from animals and plants to microorganisms, including bacteria and archaea. Since Dmitri Ivanovsky's ...

, bacteria,

fungi A fungus ( : fungi or funguses) is any member of the group of eukaryotic organisms that includes microorganisms such as yeasts and molds, as well as the more familiar mushrooms. These organisms are classified as a kingdom, separately from ...

, and

parasites Parasitism is a close relationship between species, where one organism, the parasite, lives on or inside another organism, the host, causing it some harm, and is adapted structurally to this way of life. The entomologist E. O. Wilson ha ...

), learning,

memory Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembered ...

, associative retrieval, self-regulation, and

fault-tolerance Fault tolerance is the property that enables a system to continue operating properly in the event of the failure of one or more faults within some of its components. If its operating quality decreases at all, the decrease is proportional to the ...

Artificial immune systems In artificial intelligence, artificial immune systems (AIS) are a class of computationally intelligent, rule-based machine learning systems inspired by the principles and processes of the vertebrate immune system. The algorithms are typically modele ...

are abstractions of the natural immune system, emphasizing these computational aspects. Their applications include computer virus detection,

anomaly detection In data analysis, anomaly detection (also referred to as outlier detection and sometimes as novelty detection) is generally understood to be the identification of rare items, events or observations which deviate significantly from the majority o ...

in a time series of data, fault diagnosis,

pattern recognition Pattern recognition is the automated recognition of patterns and regularities in data. It has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics ...

, machine learning, bioinformatics, optimization,

robotics Robotics is an interdisciplinary branch of computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrate ...

and

control Control may refer to: Basic meanings Economics and business * Control (management), an element of management * Control, an element of management accounting * Comptroller (or controller), a senior financial officer in an organization * Controllin ...

Membrane computing

Membrane computing Membrane computing (or MC) is an area within computer science that seeks to discover new computational models from the study of biological cells, particularly of the cellular membranes. It is a sub-task of creating a cellular model. Membrane comput ...

investigates computing models abstracted from the compartmentalized structure of living cells effected by membranes.Paun, G
Membrane Computing: An Introduction
Springer, 2002 A generic membrane system (P-system) consists of cell-like compartments (regions) delimited by ''membranes'', that are placed in a nested hierarchical structure. Each membrane-enveloped region contains objects, transformation rules which modify these objects, as well as transfer rules, which specify whether the objects will be transferred outside or stay inside the region. Regions communicate with each other via the transfer of objects. The computation by a membrane system starts with an initial configuration, where the number (

multiplicity Multiplicity may refer to: In science and the humanities * Multiplicity (mathematics), the number of times an element is repeated in a multiset * Multiplicity (philosophy), a philosophical concept * Multiplicity (psychology), having or using mult ...

) of each object is set to some value for each region ( multiset of objects). It proceeds by choosing, nondeterministically and in a maximally parallel manner, which rules are applied to which objects. The output of the computation is collected from an ''a priori'' determined output region. Applications of membrane systems include machine learning, modelling of biological processes (

photosynthesis Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities. Some of this chemical energy is stored i ...

, certain

signaling pathways Signal transduction is the process by which a chemical or physical signal is transmitted through a cell as a series of molecular events, most commonly protein phosphorylation catalyzed by protein kinases, which ultimately results in a cellula ...

quorum sensing In biology, quorum sensing or quorum signalling (QS) is the ability to detect and respond to cell population density by gene regulation. As one example, QS enables bacteria to restrict the expression of specific genes to the high cell densities at ...

in bacteria, cell-mediated

immunity Immunity may refer to: Medicine * Immunity (medical), resistance of an organism to infection or disease * ''Immunity'' (journal), a scientific journal published by Cell Press Biology * Immune system Engineering * Radiofrequence immunity desc ...

), as well as computer science applications such as

computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...

public-key cryptography Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic alg ...

, approximation and

sorting algorithms In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is import ...

, as well as analysis of various computationally hard problems.

Amorphous computing

In biological organisms,

(the development of well-defined shapes and functional structures) is achieved by the interactions between cells guided by the genetic ''program'' encoded in the organism's DNA. Inspired by this idea, amorphous computing aims at engineering well-defined shapes and patterns, or coherent computational behaviours, from the local interactions of a multitude of simple unreliable, irregularly placed, asynchronous, identically programmed computing elements (particles).Abelson, H., Allen, D., Coore, D., Hanson, C., Homsy, G., Knight Jr., T., Nagpal, R., Rauch, E., Sussman, G., Weiss, R
Amorphous computing
Communications of the ACM 43, 5 (May 2000), 74-82 As a programming paradigm, the aim is to find new programming techniques that would work well for amorphous computing environments. Amorphous computing also plays an important role as the basis for " cellular computing" (see the topics

synthetic biology Synthetic biology (SynBio) is a multidisciplinary area of research that seeks to create new biological parts, devices, and systems, or to redesign systems that are already found in nature. It is a branch of science that encompasses a broad ran ...

and cellular computing, below).

Morphological computing

The understanding that the morphology performs computation is used to analyze the relationship between morphology and control and to theoretically guide the design of robots with reduced control requirements, has been used in both robotics and for understanding of cognitive processes in living organisms, se
Morphological computation
and .Pfeifer, R. and Füchslin R.
Morphological Computing
(starts at p.11), 2013

Cognitive computing

Cognitive computing CC is a new type of computing, typically with the goal of modelling of functions of human sensing, reasoning, and response to stimulus, see

Cognitive computing Cognitive computing (CC) refers to technology platforms that, broadly speaking, are based on the scientific disciplines of artificial intelligence and signal processing. These platforms encompass machine learning, reasoning, natural languag ...

and .Pfeifer, R. and Bondgard, J.
How the body shapes the way we think: a new view of intelligence
MIT Press, 2006 Cognitive capacities of present-day cognitive computing are far from human level. The same info-computational approach can be applied to other, simpler living organisms. Bacteria are an example of a cognitive system modelled computationally, see Eshel Ben-Jacob an
Microbes-mind

Synthesizing nature by means of computing

Artificial life

Artificial life Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry ...

(ALife) is a research field whose ultimate goal is to understand the essential properties of life organisms Langton, C., editor. Artificial Life. Addison-Wesley Longman, 1990 by building, within electronic computers or other artificial media, ''

ab initio ''Ab initio'' ( ) is a Latin term meaning "from the beginning" and is derived from the Latin ''ab'' ("from") + ''initio'', ablative singular of ''initium'' ("beginning"). Etymology Circa 1600, from Latin, literally "from the beginning", from ab ...

'' systems that exhibit properties normally associated only with living organisms. Early examples include Lindenmayer systems (L-systems), that have been used to model plant growth and development. An L-system is a parallel rewriting system that starts with an initial word, and applies its rewriting rules in parallel to all letters of the word.Rozenberg, G. and Salomaa, A
The Mathematical Theory of L Systems
Academic Press, 1980 Pioneering experiments in artificial life included the design of evolving "virtual block creatures" acting in simulated environments with realistic features such as

kinetics Kinetics ( grc, κίνησις, , kinesis, ''movement'' or ''to move'') may refer to: Science and medicine * Kinetics (physics), the study of motion and its causes ** Rigid body kinetics, the study of the motion of rigid bodies * Chemical ki ...

, dynamics,

gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...

collision In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word ''collision'' refers to incidents in which two or more objects collide with great fo ...

, and

friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of ...

.Brooks. R
Artificial life: from robot dreams to reality
''Nature'' 406 (2000), 945-947 These artificial creatures were selected for their abilities endowed to swim, or walk, or jump, and they competed for a common limited resource (controlling a cube). The simulation resulted in the evolution of creatures exhibiting surprising behaviour: some developed hands to grab the cube, others developed legs to move towards the cube. This computational approach was further combined with rapid manufacturing technology to actually build the physical robots that virtually evolved.Lipson, P., Pollack, J

''Nature'' 406 (2000), 974-978 This marked the emergence of the field of mechanical artificial life. The field of

explores a biological implementation of similar ideas. Other research directions within the field of artificial life include artificial chemistry as well as traditionally biological phenomena explored in artificial systems, ranging from computational processes such as co-evolutionary adaptation and development, to physical processes such as growth,

, and self-repair.

Nature-inspired novel hardware

All of the computational techniques mentioned above, while inspired by nature, have been implemented until now mostly on traditional

. In contrast, the two paradigms introduced here, molecular computing and quantum computing, employ radically different types of hardware.

Molecular computing

Molecular computing (a.k.a. biomolecular computing, biocomputing, biochemical computing,

) is a computational paradigm in which data is encoded as

biomolecules A biomolecule or biological molecule is a loosely used term for molecules present in organisms that are essential to one or more typically biological processes, such as cell division, morphogenesis, or development. Biomolecules include lar ...

such as DNA strands, and molecular biology tools act on the data to perform various operations (e.g., arithmetic or

logical operations In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary c ...

). The first experimental realization of special-purpose molecular computer was the 1994 breakthrough experiment by

Leonard Adleman Leonard Adleman (born December 31, 1945) is an American computer scientist. He is one of the creators of the RSA encryption algorithm, for which he received the 2002 Turing Award, often called the Nobel prize of Computer science. He is also kno ...

who solved a 7-node instance of the Hamiltonian Path Problem solely by manipulating DNA strands in test tubes.Adleman, L
Molecular computation of solutions to combinatorial problems
. ''Science'' 266 (1994), 1021-1024 DNA computations start from an initial input encoded as a DNA sequence (essentially a sequence over the four-letter alphabet ), and proceed by a succession of bio-operations such as cut-and-paste (by

restriction enzymes A restriction enzyme, restriction endonuclease, REase, ENase or'' restrictase '' is an enzyme that cleaves DNA into fragments at or near specific recognition sites within molecules known as restriction sites. Restriction enzymes are one class o ...

and

ligases In biochemistry, a ligase is an enzyme that can catalyze the joining (ligation) of two large molecules by forming a new chemical bond. This is typically via hydrolysis of a small pendant chemical group on one of the larger molecules or the enzym ...

), extraction of strands containing a certain subsequence (by using Watson-Crick complementarity), copy (by using

polymerase chain reaction The polymerase chain reaction (PCR) is a method widely used to rapidly make millions to billions of copies (complete or partial) of a specific DNA sample, allowing scientists to take a very small sample of DNA and amplify it (or a part of it) ...

that employs the polymerase enzyme), and read-out.Kari, L
DNA computing - the arrival of biological mathematics
The Mathematical Intelligencer 19, 2 (1997) 9-22 Recent experimental research succeeded in solving more complex instances of

NP-complete In computational complexity theory, a problem is NP-complete when: # it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying ...

problems such as a 20-variable instance of

3SAT In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies ...

, and wet DNA implementations of finite state machines with potential applications to the design of smart drugs. Selfassemble Sierpinski

One of the most notable contributions of research in this field is to the understanding of

.Reif, J. and LaBean, T
Autonomous programmable biomolecular devices using self-assembled DNA nanostructures
Communications of the ACM 50, 9 (Sept. 2007), 46-53 Self-assembly is the bottom-up process by which objects autonomously come together to form complex structures. Instances in nature abound, and include atoms binding by chemical bonds to form molecules, and molecules forming

crystals A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...

macromolecules A macromolecule is a very large molecule important to biophysical processes, such as a protein or nucleic acid. It is composed of thousands of covalently bonded atoms. Many macromolecules are polymers of smaller molecules called monomers. The ...

. Examples of self-assembly research topics include self-assembled DNA nanostructuresSeeman, N
Nanotechnology and the double helix
Scientific American Reports, 17. 3 (2007), 30-39 such as Sierpinski trianglesRothemund, P., Papadakis, N., Winfree, E
Algorithmic self-assembly of DNA Sierpinski triangles
''PLoS Biology'' 2, 12 (December 2004) or arbitrary nanoshapes obtained using the

DNA origami DNA origami is the nanoscale folding of DNA to create arbitrary two- and three-dimensional shapes at the nanoscale. The specificity of the interactions between complementary base pairs make DNA a useful construction material, through design of ...

Rothemund, P
Folding DNA to create nanoscale shapes and patterns
''Nature'' 440 (2006) 297-302. technique, and DNA nanomachinesBath, J., Turberfield, A

Nature Nanotechnology 2 (May 2007), 275-284 such as DNA-based circuits ( binary counter, bit-wise cumulative XOR), ribozymes for logic operations, molecular switches ( DNA tweezers), and autonomous molecular motors ( DNA walkers). Theoretical research in molecular computing has yielded several novel models of DNA computing (e.g. splicing systems introduced by Tom Head already in 1987) and their computational power has been investigated.Paun, G., Rozenberg, G., Salomaa, A. DNA Computing: New Computing Paradigms. Springer, 1998 Various subsets of bio-operations are now known to be able to achieve the computational power of

Turing machines A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algor ...

Quantum computing

A quantum computerHirvensalo, M. Quantum Computing, 2nd Ed. Springer, 2004 processes data stored as quantum bits (

qubits In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, ...

), and uses quantum mechanical phenomena such as superposition and entanglement to perform computations. A qubit can hold a "0", a "1", or a quantum superposition of these. A quantum computer operates on qubits with

quantum logic gates In physics, a quantum (plural quanta) is the minimum amount of any physical entity ( physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizat ...

. Through Shor's polynomial algorithm for factoring integers, and

Grover's algorithm In quantum computing, Grover's algorithm, also known as the quantum search algorithm, refers to a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output ...

for quantum database search that has a quadratic time advantage, quantum computers were shown to potentially possess a significant benefit relative to electronic computers.

Quantum cryptography Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution ...

is not based on the complexity of the computation, but on the special properties of

quantum information Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both t ...

, such as the fact that quantum information cannot be measured reliably and any attempt at measuring it results in an unavoidable and irreversible disturbance. A successful open air experiment in quantum cryptography was reported in 2007, where data was transmitted securely over a distance of 144 km.Ursin, R. et al
Entanglemen-based quantum communication over 144km
Nature Physics 3 (2007) 481-486 Quantum teleportation is another promising application, in which a quantum state (not matter or energy) is transferred to an arbitrary distant location. Implementations of practical quantum computers are based on various substrates such as ion-traps,

superconductors Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...

nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...

, etc. As of 2006, the largest quantum computing experiment used liquid state nuclear magnetic resonance quantum information processors, and could operate on up to 12 qubits.Negrevergne, C. et al
Benchmarking quantum control methods on a 12-qubit system
''Physical Review Letters'' 96:art170501, 2006

Nature as information processing

The dual aspect of natural computation is that it aims to understand nature by regarding natural phenomena as information processing. Already in the 1960s, Zuse and Fredkin suggested the idea that the entire universe is a computational (information processing) mechanism, modelled as a cellular automaton which continuously updates its rules. A recent quantum-mechanical approach of Lloyd suggests the universe as a quantum computer that computes its own behaviour, while Vedral Vedral, V. ecoding Reality: The Universe as Quantum Information Oxford University Press, 2010 suggests that information is the most fundamental building block of reality. The universe/nature as computational mechanism is elaborated in, exploring the nature with help of the ideas of computability, whilst, based on the idea of nature as network of networks of information processes on different levels of organization, is studying natural processes as computations (information processing). The main directions of research in this area are systems biology,

and cellular computing.

Systems biology

Computational systems biology (or simply systems biology) is an integrative and qualitative approach that investigates the complex communications and interactions taking place in biological systems. Thus, in systems biology, the focus of the study is the interaction networks themselves and the properties of biological systems that arise due to these networks, rather than the individual components of functional processes in an organism. This type of research on organic components has focused strongly on four different interdependent interaction networks:Cardelli, L
Abstract machines of systems biology
Bulletin of the EATCS 93 (2007), 176-204 gene-regulatory networks, biochemical networks, transport networks, and carbohydrate networks.

Gene regulatory networks A gene (or genetic) regulatory network (GRN) is a collection of molecular regulators that interact with each other and with other substances in the cell to govern the gene expression levels of mRNA and proteins which, in turn, determine the fun ...

comprise gene-gene interactions, as well as interactions between genes and other substances in the cell.

Gene In biology, the word gene (from , ; "... Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a b ...

s are transcribed into messenger RNA (mRNA), and then translated into

protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, res ...

s according to the

genetic code The genetic code is the set of rules used by living cells to translate information encoded within genetic material ( DNA or RNA sequences of nucleotide triplets, or codons) into proteins. Translation is accomplished by the ribosome, which links ...

. Each gene is associated with other DNA segments ( promoters, enhancers, or silencers) that act as

binding site In biochemistry and molecular biology, a binding site is a region on a macromolecule such as a protein that binds to another molecule with specificity. The binding partner of the macromolecule is often referred to as a ligand. Ligands may includ ...

s for activators or repressors for

gene transcription Transcription is the process of copying a segment of DNA into RNA. The segments of DNA transcribed into RNA molecules that can encode proteins are said to produce messenger RNA (mRNA). Other segments of DNA are copied into RNA molecules called ...

. Genes interact with each other either through their gene products (mRNA, proteins) which can regulate gene transcription, or through small RNA species that can directly regulate genes. These gene-gene interactions, together with genes' interactions with other substances in the cell, form the most basic interaction network: the

gene regulatory network A gene (or genetic) regulatory network (GRN) is a collection of molecular regulators that interact with each other and with other substances in the cell to govern the gene expression levels of mRNA and proteins which, in turn, determine the fun ...

s. They perform information processing tasks within the cell, including the assembly and maintenance of other networks. Models of gene regulatory networks include random and probabilistic Boolean networks, asynchronous automata, and

network motif Network motifs are recurrent and statistically significant Subgraph (graph theory), subgraphs or patterns of a larger complex network, graph. All networks, including biological networks, social networks, technological networks (e.g., computer netw ...

s. Another viewpoint is that the entire genomic regulatory system is a computational system, a ''genomic computer''. This interpretation allows one to compare human-made electronic computation with computation as it occurs in nature.Istrail, S., De-Leon, B-T., Davidson, E
The regulatory genome and the computer
Developmental Biology 310 (2007), 187-195 In addition, unlike a conventional computer, robustness in a genomic computer is achieved by various

feedback mechanism Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handled ...

s by which poorly functional processes are rapidly degraded, poorly functional cells are killed by apoptosis, and poorly functional organisms are out-competed by more fit species. Biochemical networks refer to the interactions between proteins, and they perform various mechanical and metabolic tasks inside a cell. Two or more proteins may bind to each other via binding of their interactions sites, and form a dynamic protein complex (

complexation A coordination complex consists of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of bound molecules or ions, that are in turn known as ''ligands'' or complexing agents. Many ...

). These protein complexes may act as

catalysts Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...

for other chemical reactions, or may chemically modify each other. Such modifications cause changes to available binding sites of proteins. There are tens of thousands of proteins in a cell, and they interact with each other. To describe such a massive scale interactions, Kohn mapsKohn, K
Molecular interaction map of the mammalian cell cycle control and DNA repair systems
Molecular Biology of the Cell 10(8) (1999) 2703-2734. were introduced as a graphical notation to depict molecular interactions in succinct pictures. Other approaches to describing accurately and succinctly protein–protein interactions include the use of textual bio-calculusNagasaki, M., Onami, S., Miyano, S., Kitano, H
Bio-calculus: its concept and molecular interaction
Genome Informatics 10 (1999) 133-143. or pi-calculus enriched with stochastic features.Regev, A., Shapiro, E
Cellular abstractions: Cells as computation
''Nature'' 419 (2002) 343

Transport network A transport network, or transportation network, is a network or graph in geographic space, describing an infrastructure that permits and constrains movement or flow. Examples include but are not limited to road networks, railways, air routes ...

s refer to the separation and transport of substances mediated by lipid membranes. Some lipids can self-assemble into biological membranes. A lipid membrane consists of a

lipid bilayer The lipid bilayer (or phospholipid bilayer) is a thin polar membrane made of two layers of lipid molecules. These membranes are flat sheets that form a continuous barrier around all cells. The cell membranes of almost all organisms and many vir ...

in which proteins and other molecules are embedded, being able to travel along this layer. Through lipid bilayers, substances are transported between the inside and outside of membranes to interact with other molecules. Formalisms depicting transport networks include membrane systems and brane calculi.Cardelli, L
Brane calculi: Interactions of biological membranes
In LNCS 3082, pages 257-280. Springer, 2005.

Synthetic biology

Synthetic biology aims at engineering synthetic biological components, with the ultimate goal of assembling whole biological systems from their constituent components. The history of synthetic biology can be traced back to the 1960s, when

François Jacob François Jacob (17 June 1920 – 19 April 2013) was a French biologist who, together with Jacques Monod, originated the idea that control of enzyme levels in all cells occurs through regulation of transcription. He shared the 1965 Nobel Prize ...

and

Jacques Monod Jacques Lucien Monod (February 9, 1910 – May 31, 1976) was a French biochemist who won the Nobel Prize in Physiology or Medicine in 1965, sharing it with François Jacob and André Lwoff "for their discoveries concerning genetic control of e ...

discovered the mathematical logic in gene regulation. Genetic engineering techniques, based on

recombinant DNA Recombinant DNA (rDNA) molecules are DNA molecules formed by laboratory methods of genetic recombination (such as molecular cloning) that bring together genetic material from multiple sources, creating sequences that would not otherwise be fo ...

technology, are a precursor of today's synthetic biology which extends these techniques to entire systems of genes and gene products. Along with the possibility of synthesizing longer and longer DNA strands, the prospect of creating synthetic genomes with the purpose of building entirely artificial synthetic organisms became a reality. Indeed, rapid assembly of chemically synthesized short DNA strands made it possible to generate a 5386bp synthetic genome of a virus.Smith, H., Hutchison III, C., Pfannkoch, C., and Venter, C
Generating a synthetic genome by whole genome assembly: X174 bacteriophage from synthetic oligonucleotides
''PNAS 100'', 26 (2003), 15440-15445. Alternatively, Smith et al. found about 100 genes that can be removed individually from the genome of ''

Mycoplasma Genitalium ''Mycoplasma genitalium'' (''MG'', commonly known as Mgen) is a sexually transmitted, small and pathogenic bacterium that lives on the mucous epithelial cells of the urinary and genital tracts in humans. Medical reports published in 2007 and 2 ...

''. This discovery paves the way to the assembly of a minimal but still viable artificial genome consisting of the essential genes only. A third approach to engineering semi-synthetic cells is the construction of a single type of RNA-like molecule with the ability of self-replication.Sazani, P., Larralde, R., Szostak, J
A small aptamer with strong and specific recognition of the triphosphate of ATP
''Journal of the American Chemical Society'', 126(27) (2004) 8370-8371 Such a molecule could be obtained by guiding the rapid evolution of an initial population of RNA-like molecules, by selection for the desired traits. Another effort in this field is towards engineering multi-cellular systems by designing, e.g., cell-to-cell communication modules used to coordinate living bacterial cell populations.Weiss, R., Knight, Jr., T
Engineered communications for microbial robotics
In LNCS 2054, pages 1-16, Springer, 2001

Cellular computing

Computation in living cells (a.k.a. cellular computing, or in-vivo computing) is another approach to understand nature as computation. One particular study in this area is that of the computational nature of gene assembly in unicellular organisms called

ciliate The ciliates are a group of alveolates characterized by the presence of hair-like organelles called cilia, which are identical in structure to eukaryotic flagella, but are in general shorter and present in much larger numbers, with a differen ...

s. Ciliates store a copy of their DNA containing functional genes in the

macronucleus A macronucleus (formerly also meganucleus) is the larger type of nucleus in ciliates. Macronuclei are polyploid and undergo direct division without mitosis. It controls the non-reproductive cell functions, such as metabolism. During conjugation, ...

, and another "encrypted" copy in the

micronucleus Micronucleus is the name given to the small nucleus that forms whenever a chromosome or a fragment of a chromosome is not incorporated into one of the daughter nuclei during cell division. It usually is a sign of genotoxic events and chromosomal i ...

. Conjugation of two ciliates consists of the exchange of their micronuclear genetic information, leading to the formation of two new micronuclei, followed by each ciliate re-assembling the information from its new micronucleus to construct a new functional macronucleus. The latter process is called gene assembly, or gene re-arrangement. It involves re-ordering some fragments of DNA ( permutations and possibly

inversion Inversion or inversions may refer to: Arts * , a French gay magazine (1924/1925) * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ...

) and deleting other fragments from the micronuclear copy. From the computational point of view, the study of this gene assembly process led to many challenging research themes and results, such as the Turing universality of various models of this process. From the biological point of view, a plausible hypothesis about the "bioware" that implements the gene-assembly process was proposed, based on template guided recombination. Other approaches to cellular computing include developing an ''

in vivo Studies that are ''in vivo'' (Latin for "within the living"; often not italicized in English) are those in which the effects of various biological entities are tested on whole, living organisms or cells, usually animals, including humans, and ...

'' programmable and autonomous finite-state automaton with '' E. coli'',Nakagawa, H., Sakamoto, K., Sakakibara, Y
Development of an ''in vivo'' computer based on Escherichia Coli
In LNCS 3892, pages 203-212, Springer, 2006 designing and constructing ''in vivo'' cellular logic gates and genetic circuits that harness the cell's existing biochemical processes (see for example Zabet NR, Hone ANW, Chu DF
Design principles of transcriptional logic circuits
. In Artificial Life XII Proceedings of the Twelfth International Conference on the Synthesis and Simulation of Living Systems, pages 186-193. MIT Press, August 2010.) and the global optimization of stomata aperture in leaves, following a set of local rules resembling a