Biomedical Signal and Data Processing Group Artificial Life Lenka Lhotska Gerstner laboratory, Department of Cybernetics CTU FEE Prague

Biomedical Signal and Data Processing Group

Artificial Life

Lenka Lhotska

Gerstner laboratory, Department of Cybernetics

CTU FEE Prague

http://[email protected]


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


Introduction (cont.)

3 forms of synthetic approachIn software – computer programs exhibiting „certain

properties“ of lifeIn wetware – hardware – robotics, nanotechnologiesReplicating and selfdeveloping macromolecules - RNA


Basic propositions of artificial life

Information – substance of life, not the material form – serves only for preservation and processing

Certain complexityTwo types of information

Non-interpreted – genotype – passed to descendants Interpreted – phenotype – source for creation of structure of a

new individualEvolution – selfreproduction, mutation, selectionSynthetic process – bottom-up: from elementary primitives controlled

by simple rules to complex structures exhibiting complex behaviour High level of parallelism of dynamics of local primitivesMutual local effects – new phenomena on the global level –

emergent behaviour – without any central controlNon-linear behaviour of elementary primitives – non-validity of the

principle of superposition


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


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


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)


Cellular automata

Von Neumann neighbourhood Moore neighbourhood (full neighb.)


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 stripThe information is copied to the offspringThe offspring splits from the original automaton


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


Game of life – LIFE (cont.)


Codd automata – 2D

E.F. Codd

CA – 8 states, von Neumann neighbourhood

4 states – structural

0 – empty cell1 – signal pathway2 – coating of the signal pathway3 – 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 – 85 = 32K

Really used rules – approx. 500


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 85 = 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


Wolfram 1D CA

Wolfram – studied properties of 1D CA

Advantages of 1D CA

Relatively small number of possible rulesIllustrative representation of successive generations in rows

The simplest case – two state system

Neighbourhood – 2 neighboursNew value of the cell determined by three old values = 8

combinations28 output combinationsResulting number of possible groups of rules = 256

256 CAs divided into 4 groups according to the complexity of behaviour


Wolfram 1D CA (cont.)

CA1 – quickly converging into one state (either 0 or 1)

CA2 – initial activity decreases, stable clusters or repeated patterns appear


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


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 disorderIncrease of entropy – in seeming contradiction to the process of

evolutionFor 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


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)


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.


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.



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°.



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



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



Plants

Axiom = ++++F

a = 22.5°

F = FF+[+F-F-F]-[-F+F+F]



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]



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]A(p+d) A(p) : p > P (R) F[+L][-L]B B (R) K



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)


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

Documents

Biomedical Signal and Data Processing Group Artificial Life Lenka Lhotska Gerstner laboratory, Department of Cybernetics CTU FEE Prague