biomedical signal and data processing group artificial life lenka lhotska gerstner laboratory,...
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Biomedical Signal and Data Processing Group
Artificial Life
Lenka Lhotska
Gerstner laboratory, Department of Cybernetics
CTU FEE Prague
http://[email protected]
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
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Introduction (cont.)
3 forms of synthetic approachIn software – computer programs exhibiting „certain
properties“ of lifeIn wetware – hardware – robotics, nanotechnologiesReplicating and selfdeveloping macromolecules - RNA
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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
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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
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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
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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)
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Cellular automata
Von Neumann neighbourhood Moore neighbourhood (full neighb.)
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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
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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
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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
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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
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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
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Wolfram 1D CA (cont.)
CA1 – quickly converging into one state (either 0 or 1)
CA2 – initial activity decreases, stable clusters or repeated patterns appear
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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
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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
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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)
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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.
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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.
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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°.
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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
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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
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Lindenmayer systems (cont.)
Plants
Axiom = ++++F
a = 22.5°
F = FF+[+F-F-F]-[-F+F+F]
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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]
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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]A(p+d) A(p) : p > P (R) F[+L][-L]B B (R) K
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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)
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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