11'3: Movement of Ants plus more Matlab, plus Artificial Life

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11.3 Movement of Ants(plus more Matlab, plus
Artificial Life)
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Movement of Ants

• Ant movement complicates the spread-of-fire
  model in a number of ways
• Each ant has an orientation (N, S, E, W)
• Each cell contains an ant, a quantity of
  pheromone (chemical deposited by ants and
  attractive to them), both, or neither
• Ant cannot move into cell occupied by another

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Ordered Pair Representation

• We can represent ant presence/absence/orientation
  using one number 0 no ant 1
  E, 2 N, 3 W, 4 Ss
• Another number can represent the concentration of
  pheromone from zero to some maximum (e.g. 5).
• Book suggests using an ordered pair (like
  Cartesian coordinate) to combine these e.g., (1,
  3) east-facing ant in a cell with a 3/5
  concentration of pheromone.

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Single-Number Representation

• Matlab prefers to have a single number in each
  cell. So we can use a two-digit number to
  represent an ordered pair (3,5) becomes 35 (0,
  2) becomes 2, etc.
• grid 10ant pheromone
• ant fix(grid/10) fix keeps integer part
• pheromone mod(grid, 10)

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Matrices and Indexing

• Weve seen how to perform operations on an entire
  matrix at once grid(rand(n)ltprobTree) 1, etc.
• What if we want to operate on individual rows,
  columns, and elements?
• grid(i, j) accesses row i, column j of grid.
• grid(i, ) accesses all columns of row i
• grid(, j) accesses all rows of column j

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Matrices and Indexing Examples
grid(2, 3) 1 a tree grows at 2,3 grid(1,
) 2 whole top row on fire
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Ranges and Indexing

• But were supposed to start with a gradient strip
  of pheromone a range like 0, 1, 2, 3, 4, 5
• In Matlab we can simply say 15
• grid(3, 48) 15
• For a vertical strip, we transpose the range
• grid(26, 4) (15)
• Lets put an arbitrarily long horizontal strip
  of gradient in an arbitrary row....

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Initializing the Gradient
phergrid zeros(n) NxN pheromone grid row
fix(randn)1 indices start at 1 len
fix(randn)1 length of gradient strip col
fix(rand(n-len))1 starting
column phergrid(row, colcollen-1) 1len
help me Obi-wan!
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Initializing the Ants

• For trees we simply did
• probTree 0.2
• grid zeros(n)
• grid(rand(n)ltprobTree)

• But here we want several possible values for each
  ant
• So we can set up a grid full of ant values, then
  zero it out where appropriate....

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Initializing the Ants
probAnt 0.2 antgrid fix(4rand(n))1 4
directions antgrid(rand(n) gt probAnt) 0
Putting it all together
grid 10antgrid phergrid
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Updating the Grid

• An ant turns in the direction of the neighboring
  cell with the greatest amount of pheromone (in a
  tie, pick one at random), then walks in that
  direction
• If theres no ant in a cell, the pheromone
  decreases by 1 at each time step, with a minimum
  value of 0.
• If an ant leaves a cell, the amount of pheromone
  increases by 1 (ant deposits pheromone).
• So long as there is an ant in a cell, the amount
  of pheromone in the cell stays constant.

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Avoiding Collisions

• For an ant facing in a given direction and about
  to walk in that direction, there are three
  potential ants in other cells that it could
  collide with.
• For example, if I am an ant facing North

NN
NE
NW
N
me
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Avoiding Collisions

• Because there are four other directions (S, E,
  W), each cell has a potential collision with 12
  others

• As a first approximation, we can ignore
  collisions e.g., cell is occupied by last ant to
  move there, and others go away (maybe replaced by
  new ones being born).

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The Big Picture Self-Organization Spontaneous
Orders

• By itself, the rules for movement of ants arent
  terribly interesting.
• What interests scientists is the spontaneous
  orders and self-organizing behaviors that emerge
  from such simple systems of rules.
• This is a profound idea that shows up in biology,
  economics, and the social sciences.

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Spontaneous Orders in Markets
Every individual...generally, indeed, neither
intends to promote the public interest, nor knows
how much he is promoting it. By preferring the
support of domestic to that of foreign industry
he intends only his own security and by
directing that industry in such a manner as its
produce may be of the greatest value, he intends
only his own gain, and he is in this, as in many
other cases, led by an invisible hand to promote
an end which was no part of his intention. -
Adam Smith, The Wealth of Nations
Adam Smith (1723-1790)
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Termite Nest-Building
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Bird Flocks
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Boids Artificial Birds

• Flocks of birds appear to be moving as a coherent
  whole, following a leader avoiding obstacles
• Can this global behavior instead be emergent from
  the local behavior of individuals birds?
• Boids (Reynolds 1986) Each boid follows three
  simple rules

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Boids Artificial Birds
Separation steer to avoid crowding local
flockmates
Alignment steer towards the average heading of
local flockmates
Cohesion steer to move toward the average
position of local flockmates
http//www.red3d.com/cwr/boids/
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Evolution of Cooperation

• Consider the Prisoners Dilemma game where you
  and I are arrested for committing a crime.
• If I defect (rat you out) and you cooperate with
  me (keep quiet), you get 10 years and I go free.
• If I cooperate and you defect, I get 10 years and
  you go free.
• If we both cooperate, we each get six months
• If we both defect, we both get five years.
• What is the best strategy?

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Evolution of Cooperation

• The best strategy is for me is to defect (same
  for you).
• If I defect, the expected value (average value)
  of my punishment is 2.5 years (0 if you
  cooperate, 5 if you defect)
• If I cooperate, the expected value of my
  punishment is 5.25 years (6 months if you
  cooperate, 10 years if you defect).
• But what if we repeat this game over and over,
  allowing each of us to remember what others did
  in previous iterations (repetitions)?

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Iterated Prisoners Dilemma

• Axelrod (1981/1984) Held a simulated tournament
  among various PD strategies submitted by
  contestants
• Strategies could be arbitrarily simple (always
  defect, always cooperate) or complicated (keep
  track of other guys last five moves, then try to
  predict what hell do next time, etc.)
• Amazingly, winning strategy was simple
  tit for tat (quid pro
  quo)
• Always cooperate with someone the first
  time.
• Subsequently, do what he did on your
  previous encounter with him.

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Iterated Prisoners Dilemma (Artificial) Life
Lessons?

• In general, most successful strategies followed
  four rules
• Be nice Dont be the first to defect
• Be provocable (dont be a sucker)
• Dont be envious dont strive for a payoff
  greater than the other players
• Dont be to clever (KISS principle)

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The Bad News People Are Naturally Envious

• Ultimatum game psychology experiment with human
  subjects (Güth et al. 1982)
• Subject A is given 10 and told to share some of
  it (in whole ) with subject B, where B knows
  how much A is given
• Optimal for A is to give B 1 and keep 9
• Typically, A will offer 3, and B will refuse to
  accept anything less (!)

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The Good News TFT is an Evolutionarily Stable
Strategy

• Q What happens when we introduce a cheater
  (always defects) into a population of TFT
  players?
• A The cheater initially gains some points by
  exploiting TFT players niceness, but soon is
  overwhelmed by subsequent TFT retribution.
• So TFT is an evolutionarily stable strategy
  (Maynard-Smith 1982)

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Evolution of Communication

• What is communication?
• Communication is the phenomenon of one organism
  producing a signal that when responded to by
  another organism confers some advantage (or the
  statistical probability of it) to the signaler or
  his group.
• - G. Burghardt (1970)
• How does a community come to share a common
  system of communication (language)?

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Evolution of Communication

• MacLennan (1990) Simulate communication by a
  simple matching game each simorg (simulated
  organism) has a private situation that it wants
  to describe to others.

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• MacLennan (1990) Simulation communication by a
  simple matching game
• To communicate a situation, the individual looks
  up its current situation in a table and emits an
  symbol into the shared environment
• Each individual then uses its own table to
  convert the shared symbol back into a guess about
  the private situation of the emitter.
• Whenever an individual matches the emitters
  situation, it and the emitter get a fitness point
• Individuals with highest fitness get to survive

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Evolution of Communication Results, Fitness
fitness
iteration
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Evolution of Communication Results, Denotation
Matrix
First iteration random association of symbols
with situations
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Evolution of Communication Results, Denotation
Matrix
Last iteration systematic association of symbols
with situations
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synonyms
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homonyms
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Quantifying Denotation (Dis)order

• Shannon Information Entropy quantifies (in
  bits) amount of disorder in a distribution

where pk is the probability of event (situation) k

• Examples
• p 0.25, .25, .25, .25, H 2.0
• p .95, .025, .0125 ,.0125 , H 0.36

Claude Shannon (1916-2001)
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Choosing the Next Generation
Fitness-Proportionate Selection use our biased
roulette wheel to favor individuals with higher
fitness, without ruling out selection of
low-fitness individuals
individuals
i1
i3
i4
i2
8
10
22
60
normalized fitnesses
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Iterating Over Generations

• A highly expressive language like Matlab may
  allow us to avoid explicit iteration (looping),
  via operators like sum, gt , etc.
• But when the current generation (population)
  depends on the previous one, we say that the
  model is inherently iterative.
• For such models we use an explicit loop,
  typically a for loop....

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Original Population Model in Matlab
growth rate k 0.1 initial population P0
100 P zeros(1, 20) P(1) P0 iterate for
t 220 P(t) P(t-1) kP(t-1) end
analytical solution Pa P0 exp(k120)
overlay plots plot(P) hold on plot(Pa, 'r') red
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Modeling Simulation Conclusions

• Cellular automata and related simulations can be
  a powerful and exciting way of exploring
  phenomena for which an actual experiment is too
  difficult or costly.
• But one must be careful not to build-in the
  very behavior that one claims is emergent.
• One must also be careful not to over-interpret
  the results.

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Potential Projects

• Implement collision avoidance in ants simulation.
• Implement Conways Game of Life in init, update
  functions.
• Implement MacLennans evolution of communication
  algorithm.