1. Biomedical Signal and Data Processing Group Artificial Life Lenka Lhotska Gerstner laboratory, Department of Cybernetics CTU FEE Prague http://cyber.felk.cvut.cz lhotska@fel.cvut.cz

2. Biomedical Signal and Data Processing Group Introduction  biology is the scientific study of life on Earth based on carbon-chain chemistry  Artificial Life („AL'' or „Alife'') - name given to a new discipline that studies "natural" life by attempting to recreate biological phenomena from scratch within computers and other "artificial" media  Alife complements the traditional analytic approach of traditional biology with a synthetic approach in which, rather than studying biological phenomena by taking apart living organisms to see how they work, one attempts to put together systems that behave like living organisms.  Artificial life amounts to the practice of „synthetic biology'' and, by analogy with synthetic chemistry, the attempt to recreate biological phenomena in alternative media will result in not only better theoretical understanding of the phenomena under study, but also in practical applications of biological principles in the technology of computer hardware and software, mobile robots, spacecraft, medicine, nanotechnology, industrial fabrication and assembly, and other vital engineering projects.  empirical research in biology - life-as-we-know-it  study of Artificial Life - life-as-it-could-be

3. Biomedical Signal and Data Processing Group Introduction (cont.)  3 forms of synthetic approach  In software – computer programs exhibiting „certain properties“ of life  In wetware – hardware – robotics, nanotechnologies  Replicating and selfdeveloping macromolecules - RNA

4. Biomedical Signal and Data Processing Group Basic propositions of artificial life  Information – substance of life, not the material form – serves only for preservation and processing  Certain complexity  Two types of information  Non-interpreted – genotype – passed to descendants  Interpreted – phenotype – source for creation of structure of a new individual  Evolution – selfreproduction, mutation, selection  Synthetic process – bottom-up: from elementary primitives controlled by simple rules to complex structures exhibiting complex behaviour  High level of parallelism of dynamics of local primitives  Mutual local effects – new phenomena on the global level – emergent behaviour – without any central control  Non-linear behaviour of elementary primitives – non-validity of the principle of superposition

5. Biomedical Signal and Data Processing Group Kinematic model  John von Neumann  Idea of self-reproducing automaton – based on a computer and additional elements:  Manipulator  Separator  Coupler  Sensor – recognizes elements and passes the information to the centre  Girders – two functions – skeleton of the whole structure and memory

6. Biomedical Signal and Data Processing Group Kinematic model (cont.)  Study of NASA  Based on von Neumann model  Self-growing lunar factory  two concepts  self-replicating – full realization of kinematic model  growing variant

7. Biomedical Signal and Data Processing Group Cellular automata  Dynamic system – discrete in time and space  Composed of regular structure of cells in N-dimensional space (frequently 2D)  Each cell – one of K possible states (frequently 2 states: 0 – dead cell, 1 – living cell)  Value in next time step (next generation) – synchronous calculation based on local transition function  Arguments of this function – current values in the cell and its neighbours (von Neumann or full neighbourhood)  Assumptions  infinite structure  paralelism  locality (new state depends only on the current state of the cell and its neighbours)  homogeneity (all cells have the same transition function)

8. Biomedical Signal and Data Processing Group Cellular automata Von Neumann neighbourhood Moore neighbourhood (full neighb.)

9. Biomedical Signal and Data Processing Group Von Neumann´s cellular automaton  200 000 cells – 29 states  Body consisting of 80 x 400 cells (components A, B and C – factory, duplicator and computer from the kinematic model)  Long outgrowth – 150 000 cells (analogy of strip at Turing machine)  Emergent behaviour: simple local cell behaviour results in complex global behaviour of the whole organism  Replication:  On one end of the body an arm slides out, a copy of original structure starts to grow  The process is controlled by commands on the strip  The information is copied to the offspring  The offspring splits from the original automaton

10. Biomedical Signal and Data Processing Group Game of life - LIFE  John Horton Conway – mathematician at University of Cambridge  CA – two states (empty and living cell) and full neighbourhood  Rules  Birth – in the neighbourhood of an empty cell there are three living cells  Survival – in the neighbourhood of a living cell two or three living cells  Death - in the neighbourhood of a living cell 0, 1, 4, 5, 6, 7 or 8 other living cells  Biological interpretation  Resulting situations  death (structure A on the following slide)  stable (in future steps constant) (structure B on the following slide)  Cyclic repetition (structure C on the following slide)  Cyclic repetition but shifted (structure D - glider on the following slide)  R-pentomino (structure E on the following slide) – stabilizes in 1103rd generation – resulting structure consists of 15 simple stable patterns, 4 cyclic structures (C) and 6 gliders

11. Biomedical Signal and Data Processing Group Game of life – LIFE (cont.)

12. Biomedical Signal and Data Processing Group Codd automata – 2D  E.F. Codd  CA – 8 states, von Neumann neighbourhood  4 states – structural  0 – empty cell  1 – signal pathway  2 – coating of the signal pathway  3 – special application, e.g. gate  4 states – functional – signal (4, 5, 6, 7)  Basic information element – tuple of signal cell and empty cell  In one generation – shift by one position  Total number of possible rules – 8 5 = 32K  Really used rules – approx. 500

13. Biomedical Signal and Data Processing Group Langton Q-loops  Based on Codd model  Simpler version of self-reproducing 2D CA – so-called Q-loops (SR-loops = Self Reproducing loops)  Total number of rules 8 5 = 32K  Used number of rules - 219  information 70 70 70 70 70 70 40 40 moving in the loop  Generations on the figures – 0, 7, 34, 69, 120, 126, 127, 137, 151, 451, 901

14. Biomedical Signal and Data Processing Group Wolfram 1D CA  Wolfram – studied properties of 1D CA  Advantages of 1D CA  Relatively small number of possible rules  Illustrative representation of successive generations in rows  The simplest case – two state system  Neighbourhood – 2 neighbours  New value of the cell determined by three old values = 8 combinations  28 output combinations  Resulting number of possible groups of rules = 256  256 CAs divided into 4 groups according to the complexity of behaviour

15. Biomedical Signal and Data Processing Group Wolfram 1D CA (cont.) CA1 – quickly converging into one state (either 0 or 1) CA2 – initial activity decreases, stable clusters or repeated patterns appear

16. Biomedical Signal and Data Processing Group Wolfram 1D CA (cont.) CA3 – apparently chaotic development prevails, the patterns resemble random noise CA4 – exhibit complex, but obvious regularity, new usually shifting structures are generated (e.g. gliders), the structures are living relatively long

17. Biomedical Signal and Data Processing Group Quantitative evaluation of dynamics of CA  Langton – quantification based on Wolfram classification of 1D CA  Focused on ability of CA to transfer information  Langton: All living organisms process information. Information is used for reproduction, food search, maintenance – keeping inner structure.  2nd law of thermodynamics – entropy is increasing in the closed system  Entropy = measure of the disorder  Increase of entropy – in seeming contradiction to the process of evolution  For evaluation of the ability of a CA system to transfer and save information – lambda parameter  Lambda = number of rules having „non-quiet“ states on their output / total number of rules  „quiet“ state – cell in quiet state having in the neighbourhood only cells in quiet states does not change its state in the next generation

18. Biomedical Signal and Data Processing Group Quantitative evaluation of dynamics of CA (cont.)  Lambda parameter – significant with large number of sets of rules when examination of all combinations is impossible  Relation between Wolfram classes and lambda parameter:  Small values of lambda – CA1 and CA2 (information is frozen, it can be kept for long time, but it is impossible to transfer it)  Large values of lambda – CA3 (information is transfered easily, even chaotically, but it is difficult to save it)  Boundary values of lambda – CA4 (transfer of information is possible, but it is not so fast that the link to its former location is lost)  First two modes are not favourable for existence of life, the third mode is favourable: life exists on the very edge of chaos (critical limit of complexity)

19. Biomedical Signal and Data Processing Group Lindenmayer systems  L-systems - a mathematical formalism proposed by the biologist Aristid Lindenmayer in 1968 as a foundation for an axiomatic theory of biological development.  several applications in computer graphics - generation of fractals and realistic modelling of plants  Central to L-systems, is the notion of rewriting, where the basic idea is to define complex objects by successively replacing parts of a simple object using a set of rewriting rules or productions. The rewriting can be carried out recursively.  The most extensively studied and the best understood rewriting systems operate on character strings.  Chomsky's work on formal grammars (1957) spawned a wide interest in rewriting systems. Subsequently, a period of fascination with syntax, grammars and their application in computer science began, giving birth to the field of formal languages.

20. Biomedical Signal and Data Processing Group Lindenmayer systems (cont.)  new type of string rewriting mechanism, subsequently termed L-systems.  essential difference between Chomsky grammars and L-systems - method of applying productions  In Chomsky grammars productions are applied sequentially, whereas in L- systems they are applied in parallel, replacing simultaneously all letters in a given word. This difference reflects the biological motivation of L-systems. Productions are intended to capture cell divisions in multicellular organisms, where many division may occur at the same time. D0L-system  The simplest class of L-systems (D0L stands for deterministic and 0-context or context-free)  Triple composed of the set of symbols V, starting non-empty word A (axiom) and set of rules P of the form X=S, where X a symbol and S a word. Word is a chain of symbols.

21. Biomedical Signal and Data Processing Group Lindenmayer systems (cont.) Fractals and graphic interpretation of strings  A state of the turtle is defined as a triplet (x, y, a), where the Cartesian coordinates (x, y) represent the turtle's position, and the angle a, called the heading, is interpreted as the direction in which the turtle is facing. Given the step size d and the angle increment b, the turtle can respond to the commands represented by the following symbols:  F Move forward a step of length d. The state of the turtle changes to (x',y',a), where x'= x + d cos(a) and y'= y + d sin(a). A line segment between points (x,y) and (x',y') is drawn.  f Move forward a step of length d without drawing a line. The state of the turtle changes as above.  + Turn left by angle b. The next state of the turtle is (x,y,a+b).  - Turn right by angle b. The next state of the turtle is (x, y,a-b).  | The turtle turns by 180°.

22. Biomedical Signal and Data Processing Group Lindenmayer systems (cont.) Koch flake  Axiom = F++F++F ( isosceles triangle)  a = 60°  F=F-F++F-F  Axiom and first four iterations  Linear magnification – 3x, thus 4 = 3D and dimension of Koch flake D = 1.2618  Circumference of the flake converges to infinity(O = 3 * 4/3 * 4/3 * 4/3 * 4/3 ), but the area has finite value that is lower than area of the circle circumscribed the original triangle

23. Biomedical Signal and Data Processing Group Lindenmayer systems (cont.) Sierpinski triangle  Axiom = FXF++FF++FF  a = 60°  F = FF X = ++FXF--FXF--FXF++  3 = 2D and D = 1.5849625  Unremoved area converges to 0 and the circumference converges to infinity.  Axiom and first four iterations

24. Biomedical Signal and Data Processing Group Lindenmayer systems (cont.) Plants  Axiom = ++++F  a = 22.5°  F = FF+[+F-F-F]-[-F+F+F]

25. Biomedical Signal and Data Processing Group Lindenmayer systems (cont.) Stochastic L-systems  Axiom = ++++F  a = 22.5°  F = (0.5) FF+[+F-F-F]-[-F+F+F] F = (0.5) FF+[+F-F]-[-F+F]

26. Biomedical Signal and Data Processing Group Lindenmayer systems (cont.) Context L-systems  1L – systems – context is represented by a single symbol K before symbol S, denoted K(S, or K after S, denoted S)K  2L – systems – context is represented by one symbol before and one after S, denoted P(S)Z  kontext predstavuje po jednom symbolu pred a za S, označuje sa P(S)Z  IL - systems or (k,l) systems – considering k symbols before and l symbols after symbol S Parametric L-systems  Axiom = A(0)  a = 30°  A(p) : p P (R) F[+L][-L]B B (R) K

27. Biomedical Signal and Data Processing Group Lindenmayer systems (cont.) Axiom = A(0) a = 45° A(p) : p>0 = A(p-1) A(p) : p = = 0 = F(1)[+A(4)][-A(4)]F(1)A(0) F(a) = F(1.23*a)

28. Biomedical Signal and Data Processing Group Interesting web pages www.alife.org www.swarm.org http://www.frams.alife.pl/ http://www.swarms.org/ http://www.alcyone.com/max/links/alife.html http://www.math.com/students/wonders/life/life.html http://psoup.math.wisc.edu/Life32.html http://www.people.nnov.ru/fractal/Life/Game.htm