Artificial Life

1
Artificial Life

• Lenka Lhotska
• Gerstner laboratory, Department of Cybernetics
• CTU FEE Prague
• http//cyber.felk.cvut.cz
• lhotska_at_fel.cvut.cz

2
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
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
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
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
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
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
Cellular automata

• Von Neumann neighbourhood Moore
  neighbourhood (full neighb.)

9
Von Neumanns 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
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
Game of life LIFE (cont.)
12
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 85 32K
• Really used rules approx. 500

13
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

14
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
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
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
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
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
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
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 XS, where X a symbol and S a word. Word
  is a chain of symbols.

21
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,ab).  
• -    Turn right by angle b. The next state
  of the turtle is (x, y,a-b).
• The turtle turns by 180.

22
Lindenmayer systems (cont.)

• Koch flake
• Axiom FFF ( isosceles triangle)  
• a 60    
• FF-FF-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
Lindenmayer systems (cont.)

• Sierpinski triangle
• Axiom FXFFFFF    
• 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
Lindenmayer systems (cont.)

• Plants
• Axiom F    
• a 22.5    
• F FFF-F-F--FFF

25
Lindenmayer systems (cont.)

• Stochastic L-systems
• Axiom F    
• a 22.5    
• F (0.5) FFF-F-F--FFF    F (0.5)
  FFF-F--FF

26
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, oznacuje 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 lt P (R) FL-LA(pd)     A(p) p gt
  P (R) FL-LB     B (R) K

27
Lindenmayer systems (cont.)

• Axiom A(0)    
• a 45   
• A(p) pgt0 A(p-1)     A(p) p 0
  F(1)A(4)-A(4)F(1)A(0)     F(a) F(1.23a) 

28
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.htm
  l
• http//psoup.math.wisc.edu/Life32.html
• http//www.people.nnov.ru/fractal/Life/Game.htm