GEOG3150 Semseter 2
Lecture 4
COMPLEXITY AND
EMERGENCE
Dr Nick Malleson
Dr Alison Heppenstall
Re-cap: last week…
Social simulation
Interest in ‘60s and again in ‘90s (with AI).
Agent-based modelling
The uses of simulation.
Explanatory vs predictive
Recap: Why is social simulation
important?
Understanding more about society through…
Testing out ideas using simulation to…
Create new knowledge, test existing theories,
create new theories and create new insight in…
A computer generated environment that…
Overcomes (some) ethical problems
Modelling Recap:
Bottom up v.s. top-down
Aggregate
Advantages
Individual-level
Ci = α + βxi + βyi + βzi
Simplicity
Homogeneous
Individuals
Very large systems
Disadvantages
Low-level dynamics
(‘smoothing out’)
Modelling interactions and
emergence
Representing complex systems
Advantages
Heterogeneity
Interactions
(Human) Behaviour
Emergence and complex
systems
Disadvantages
Difficult to create
Computationally expensive
Difficult to define (choose
important variables)
Practical recap..
We’ll spend ~5 minutes going over some of the
material covered in the practical.
How do you do the following:
Change the value of a variable?
Ask the turtles to change their colour?
Ask the blue turtles to move to the point (5,14)? (Then review this
diagram).
Ask the turtles to do more than one thing (e.g. turn blue and then move
forward)
Make a procedure called ‘move-turtles’ ?
Call the procedure from the ‘go’ procedure?
Make a global variable with a slider
Lecture 4
These are all key concepts!
Emergence
Cellular Automata and the Game of Life
Non-linear dynamics
Complexity
Chaos
Readings
Flake, G. (1998) The Computational Beauty of Nature. MIT Press
Wolfram, S. (2002). A New Kind of
Science. Wolfram Media
Railsback, S.F., 2012. Agent-Based and Individual-Based Modeling: A Practical Introduction.
Princeton University Press, New Jersey. (Page 101+)
Emergence: What is it?
“A property of a collection of simple sub-units that comes about through the
interactions of the subunits and is not a property of any single subunit”
- Gary Flake
“The way that complex systems and patterns arise
out of a multiplicity of relatively simple interactions”
- Wikipedia
“The whole is greater than the
sum of its parts.”
- Aristotle (?)
Attribution: Discott
https://en.wikipedia.org/
wiki/User:Discott
Attribution: Yewenyi at the English language Wikipedia
https://en.wikipedia.org/wiki/User:Yewenyi
Emergence questions
When watching the video, think about:
If there is no leader, how are flocks etc. controlled?
List some of the organisms that demonstrate emergent
behaviour
Can you think of any other examples of emergent phenomena
Emergence: What is it?
http://www.pbs.org/wgbh/nova/
nature/emergence.html
http://www.youtube.com/w
atch?v=aEaZHWXmbRw
(up to 4:50)
Emergence: What is it?
Simple rules -> complex outcomes
In the past, we have assumed that complex
phenomena are driven by a complex
mechanism
This is not always the case
Possible to prove the with simple computer
programs
Agent-based models are one example, others
to follow…
Emergence:
A new kind of science?
“I even have increasing evidence that thinking
in terms of simple programs will make it
possible to construct a single truly fundamental
theory of physical, from which space, time,
quantum mechanics and all the other known
features of our universe will emerge.”
- Wolfram (2002)
Game time!
http://www.icosystem.com/labsdemos/the-game/
Rules
Everyone randomly selects 2 individuals – person A and
person B.
Now move so that you always keep A in between yourself
and B – so that A is your protector from B.
At some point Nick will say ‘stop’. Then you become the
protector, and need to move so that you keep yourself
between A and B.
Health and Safety
Slippery, uneven ground, please be careful
Don’t leave the field
This isn’t compulsory, so if you don’t have sensible shoes (or
don’t want to come) you can wait here.
Lecture 4
Emergence
Cellular Automata and the Game of Life
Non-linear dynamics
Complexity
Chaos
An Example of Emergence:
Cellular Automata
Not dissimilar to an agent-based model.
Useful here to demonstrate emergence
Consist of a grid of cells
(similar to NetLogo patches)
Rules drive behaviour of cells
E.g. If more than two neighbours repaint their house, I will repaint
mine.
E.g. If farmers around me start to grow barley, I will grow maize
All cells driven by the same rules
But cells can be in different states
An Example of Emergence:
Cellular Automata
Simple rules can produce
complicated patterns.
E.g. fractals
Cellular Automata in Geography
Great for physical geographical systems
Land use / land cover change
Forest fires
Water systems
.. etc .. (look up some examples yourselves)
NetLogo Demos:
Voting (people’s votes are influenced by their neighbours)
Fire (spread of forest fires)
Percolation (oil spreading through earth)
What is are the main differences between a cellular
automata and an agent-based model?
The Game of Life
A cellular automata
Beautiful example of simple rules leading to
complex outcomes
Cells can be alive (black) or dead (white)
Rules for each cell:
If dead, and alive neighbours = 3 → Alive
If alive, and alive neighbours < 2 → Die of loneliness
If alive and alive neighbours > 3 → Die of overcrowding
Otherwise, stays as it is.
The Game of Life in NetLogo
‘Life’ model
The Game of Life
Gliders
A glider is a pattern that
travels across the board
in the Game of Life
Very useful!
Can transmit information
across the world
Building blocks for many
other objects (by colliding
in a particular way)
The Game of Life
Glider Gun
A pattern that
automatically
creates gliders
Running the
model
Initial
configuration
See https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
Image attributed to Kieff (https://en.wikipedia.org/wiki/User:Kieff)
The Game of Life
Spaceships
Lightweight spaceship
David Eppstein's weekender
Loads of other examples ...
For more information, see: http://www.conwaylife.com/wiki/Spaceship
The Game of Life
So what?!
This might all seem fairly pointless …
… the really interesting stuff happens when
these different patterns are combined ...
... and they start to produce patterns that
look like a living thing …
The Game of Life
Examples
Use software called ‘Golly’
http://golly.sourceforge.net/
Examples
Breeders
Create new patterns
Life -> breeders -> p90 rake factory
Life -> breeders -> space filler
Others
Life-like -> Replicator
Life-like -> Spiral growth
Life-like -> Coral
Remember the key message -> these complex, life-like patterns
emerge through the application of three simple rules.
Emergence: why is it important?
Key message: Complex structures can
emerge from simple rules
Emergence is hard to anticipate
Cannot be deduced from solely analysis of
individuals’ behaviour
Emergence is a characteristic of complex
systems
Emergence: why is it important?
Global (macro) level patterns are the result of
micro interactions.
Individual-level modelling is focused on
understanding how macro-level patterns
emerge from micro-level through the process of
simulation.
Macro: global scale e.g. the largest scale you
are modelling at e.g. regional, country
Micro: small scale e.g. individuals, households
Real Example: Segregation –
Schelling
Thomas Schelling (Harvard) looked at racial
segregation.
You will have experimented with his model in
the last practical
Initially 1D, then 2D, cellular automata / ABM
Cells either 1 or 0 (“black” or “white”).
If neighbourhood > x% of another colour,
move to nearest area where this isn’t true.
NetLogo: Demonstration
What do you think happens when 35%,
50% and 80% preferences are selected?
35%:
50%:
80%:
Schelling Results
Even with low individual preferences for
neighbour similarity, segregation develops.
35% preference
50% preference
80% preference
(Also, if preference is too high, then no one is
satisfied)
Lecture 4
Emergence
Cellular Automata and the Game of Life
Non-linear dynamics
Complexity
Chaos
Linear Systems
Linear: the output of a system is linearly proportional to the inputs
Example:
You have a population of 10 bunnies
Each bunny will have 4 bunny babies
You can work out how many bunnies there will be in 3 generations:
Generation 1: 10 bunnies.
Generation 2: 10 X 4 = 40 bunnies.
Generation 3: 10 X 4 X 4 = 160 bunnies
Generation n: 10 X (n-1) bunnies
This is an example of LINEAR system.
Linear Systems
Example of a linear system.
With bunnies!
Now, we increase the number
of bunnies per parent.
You have a population of 10
bunnies
You have a population of 10
bunnies
Each bunny will have 4 bunny
babies
Each bunny will have 6 bunny
babies
You can work out how many
bunnies there will be in 3
generations:
You can work out how many
bunnies there will be in 3
generations:
Generation 1: 10 bunnies.
Generation 2: 10 X 4 = 40 bunnies.
Generation 3: 10 X 4 X 4 = 160
bunnies
Generation n: 10 X 4(n-1) bunnies
Generation 1: 10 bunnies.
Generation 2: 10 X 6 = 60 bunnies.
Generation 3: 10 X 6 X 6 = 360
bunnies
Generation n: 10 X 6(n-1) bunnies
If we change the model inputs, there is a linear change in the outputs
Non-linear: A bunnies tale
The bunny population continues to grow in a linear
fashion.
All those tasty bunnies don’t go unnoticed by predators
As the predator population thrives, the bunnies diminish.
However, as the predator’s food is scarce, their
population begins to fail. The bunny population recovers.
The cycle begins again.
Now, if we change the bunny
growth rate, what will happen?
Non-linearity in
wolf-sheep model
Demo: wolf-sheep
predation
Run the model (with
grass)
Now, I am going to kill some of the sheep, what
will happen?
Non-linearity in the wolf-sheep
model
Unlike our bunny population, removing sheep
has unexpected effects
Changing model inputs has a non-linear
impact on the model outcomes
We cannot predict how the system will behave
(At least not very far into the future)
Understanding the interactions between
wolves, sheep and grass is the key
Non-linearity
In general, non-linear systems are any system
where the inputs are not linearly proportional to
the outputs. E.g.:
Thresholds
Rule-based
Random etc.
Non-linearity leads to “chaos” /chaotic dynamics
Irregular dynamics where the system keeps changing
without exact repetition.
More on “chaos” later…
Nonlinearity – A
Mathematical Example
Lotka-Volterra equations
Mathematical representation of predator-prey system
x is the number of prey
y is the number of predators
α, β, ζ, δ are parameters
The population fluctuates
alpha = 2
beta = 0.5
gamma = 0.2
delta = 0.6
Nonlinearity – Another
Mathematical Example
The logistic map
xn1  rxn (1  xn )
Mathematical representation of a population growth
model
xn -> ratio of existing population to the maximum
possible population at year n
r -> reproduction or starvation, depending on population
size
What happens as r increases?
Logistic Map
What
happens as
r increases?
The program that I
demonstrated in the lecture
was made by Dan Olner. You
can run it yourself here:
http://www.personal.leeds.ac.u
k/~geodo/exploringchaos/
Attributiong: Gisling (http://commons.wikimedia.org/wiki/User:Gisling) on Wikipedia
Lecture 4
Emergence
Cellular Automata and the Game of Life
Non-linear dynamics
Complexity
Chaos
Flocks – AgentBased Swarms
Result of agents working
together to produce groups
that follow each other
E.g. herds of animals, flocks
of birds, or schools of fish.
http://www.youtube.com/watch?v=qJjeHLcbQJ0
Question
How is the flock controlled?
Boids
Scientists have puzzled over how flocks are
controlled
A solution has been offered by Craig Reynolds
(1986) – a simulation of flocking behaviour
Each agent has the following rules…
Avoid colliding with your neighbour most of all.
Fly in the average direction of your neighbours.
Try to move into the centre of the flock (to prevent being
eaten).
The seemingly realistic flocking patterns suggest that
it is an emergent phenomena with no ‘leader’.
Flocks – How they act
http://www.youtube.com/watch?v=GUkjC-69vaw
Uses of flocking agents
Simulating how crowds move.
Popular Post-Hillsborough.
Notting Hill Carnival
MausHouse
Lecture on this later…
Bringing it all together …
Complex Systems
Systems that exhibit the features we have seen in this lecture can be
called ‘complex’.
Complex systems are
Non-linear
Driven by large numbers of variables
Have emergence as a key feature
Can demonstrate spatial and temporal variance
Note: Complex ≠ complicated
e.g. the Lotka–Volterra equation
But…
“The jury is still out as to how the word ‘complexity’ should be defined”
(Flake, 1998, p 135)
Lecture 4
Emergence
Cellular Automata and the Game of Life
Non-linear dynamics
Complexity
Chaos
Chaos
Chaotic systems
Tiny changes can have
huge impacts
The ‘butterfly effect’
Example:
The logistic map (in
earlier slides)
Edward Lorenz’s 1960s
weather simulation
Photo attributed to Gianfranco Reppucci on Flickr
http://www.flickr.com/photos/giefferre/4446877066/
Behaviour is deterministic
But very difficult to predict in the long term
Chaos
One lecture (or even a whole course) cannot do
justice to this new, potentially revolutionary area of
scientific research.
Do some reading! You’ll find it fascinating
(And it will be obvious in the exam who really
understands all this… )
Complex Geographical Systems
Traditional modelling techniques cannot handle
the defining features of complex systems
Particularly non-linearity and emergence
But most geographical systems are complex
systems!
Individual-level modelling techniques are
showing great potential for modelling
geographical systems.
Complex Geographical Systems
The weather
Chaotic system (tiny changes lead to dramatic effects,
‘discovered’ by Edward Lorenz)
Ensemble modelling to manage the chaos
Nonlinear partial differential equations, similar to a cellular
automata (I think!)
Crowds
Uncountable human-human and human-environment
interactions
What causes protests to become riots?
… more on these practical applications later in the
course…
Issues – Geographers Can Save
the World
There are several major questions we’d want to ask
of geographical systems if we could.
Stability: does the system have a dynamic equilibrium
or does it fluctuate?
Robustness: can the system withstand shocks and still
produce sensible outputs?
Sensitivity: will a small perturbation produce chaos?
If we can identify complexity within systems, we can:
Understand them better
Manipulate them to our own requirements
Make better predictions
Summary
Emergence: sum is greater than the parts
Bottom-up / individual-level modelling is
focused on understanding how macro-level
patterns emerge from micro-level through the
process of simulation.
Non-linearity: Relationship between two
variables is not linear (Predator-prey)
Complex systems: Exhibit non-linearity and
emergence. Very difficult to predict!
Chaos: Small changes lead to huge impacts
Further reading / watching
To really have a chance of understanding these concepts, you’ll need to do
some more research.
The resources below are a good place to start.
Also see the list on the course website:
http://www.geog.leeds.ac.uk/courses/level3/geog3150/lectures/lecture4/
Igor Nikolic, Complex Adaptive Systems TED talk
http://tedxtalks.ted.com/video/TEDxRotterdam-Igor-Nikolic-Comp
Read a relevant chapter in my favourite academic book
Flake, G. (1998) The Computational Beauty of Nature. MIT Press
Systems of Systems (IBM)
http://www.youtube.com/watch?v=h2br2_twHfw
Clips from a BBC Documentary about chaos (ideas about chaos are closely
related to complex systems)
On the VLE (not publicly available) https://vlebb.leeds.ac.uk/bbcswebdav/xid-4312172_2
A full-legth BBC documentary: “The Secret Life of Chaos”
Available on Box of Broadcasts:
http://bobnational.net/record/21567
Next week
How to model interactions and behaviour.
Seminar – The Ethics of Individual-Level
Modelling
Promises something different.
Two short readings.
http://www.geog.leeds.ac.uk/courses/level3/geo
g3150/seminars/seminar2/
A video to finish...
http://tedxtalks.ted.com/video/TEDxRotterdam-Igor-Nikolic-Comp