Lecture 02 - Complex systems Flashcards

1
Q

What are the 5 parts that a complex system might have? (CLOSE)

A
  • Small ”simple” components
  • Locally correlated and interacting parts
  • Self-organization (over time)
  • “The whole is more than the sum of its parts”
  • Emergence (over scale)
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2
Q

Cellular automata

What are automata?

A

a theoretical machine that changes its internal state based on inputs and its previous state

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3
Q

Cellular automata

What are cellular automata (CA)?

A

A set of automata arranged along a regular spatial grid, whose states are simultaneously updated by a uniformly applied state-transition function that refers to the states of their neighbours

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4
Q

Cellular automata

Who invented cellular automata (CA)?

A

John von Neumann

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5
Q

Cellular automata

What is the definition of cellular automata (CA)? (5 things)

A
  • Simplified “universe”
  • D-dimensional grid of cells (bounded or unbounded)
  • Time and space are discrete
  • Laws of the “universe” is a set of rules (finite state machine, FSM),
  • All cells are updated simultaneously at every time step
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6
Q

Cellular automata

What is a CA’s cell neighbourhood?

A

The cells close to it (depending on its neighbourhood radius).

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7
Q

Cellular automata

What is a state transition function? (CA)

A

The function that updates a single cell’s state during a time step update.

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8
Q

Cellular automata

What’s the difference between a von Neumann and a Moore neighbourhood?

A

(See image)

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9
Q

Cellular automata

What are these kinds of neighbourhoods called?

A

Left: Von Neumann neighbourhood
Right: Moore neighbourhood

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10
Q

Cellular automata

What does it mean when a cell is quiescent?

A

It remains in the same state if all neighbours are quiescent

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11
Q

Cellular automata

What does it mean when a cell is active?

A

It’s non-quiescent; that is, it can change states.

E.g. in the game of life, an active cell is a cell that ides of loneliness; its result might be quiescent afterwards.

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12
Q

Cellular automata

In CA, what do boundary conditions belong to?

A

They are properties of the CA grid.

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13
Q

Cellular automata

What are the four CA boundary conditions called?

A
  • No Boundaries
  • Periodic
  • Cut-off
  • Fixed
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14
Q

Cellular automata

What are the “No Boundaries” Boundary conditions?

A

infinite space filled with quiescent cells

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15
Q

Cellular automata

What are the “Periodic boundaries” Boundary conditions?

A

wrap around

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16
Q

Cellular automata

What are the “Cut-off boundaries” Boundary conditions?

A

no neighbours at the edge

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17
Q

Cellular automata

What are the “Fixed boundaries” Boundary conditions?

A

fixed state at the edge

18
Q

Cellular automata

(Double check answer) What is a Totalistic CA?

A

Totalistic CA is CA where a cell’s transition depends only on the neighbourhood, e.g. sum of neighbours.

19
Q

Cellular automata

What is the Majority rule? (binary CA rules)

A

Next state is the majority in the neighborhood

20
Q

Cellular automata

What is the behaviour of Majority rule? (binary CA rules)

A

Self-organizes into geographically separated patches

21
Q

Cellular automata

What is another name for the Parity rule? (binary CA rules)

A

The XOR rule

22
Q

Cellular automata

What is the behaviour of the Parity rule? (binary CA rules)

A

Any pattern in the initial configuration replicates and propagates

23
Q

Cellular automata

What are the four rules for Game of Life called?

A
  • Happiness
  • Overcrowding
  • Loneliness
  • Reproduction
24
Q

Cellular automata

What is the loneliness rule in the Game of Life?

A

Alive cells with fewer than 2 alive neighbours die

25
Q

Cellular automata

What is the overcrowding rule in the Game of Life?

A

Alive cells with 4+ alive neighbours die

26
Q

Cellular automata

What is the happiness rule in the Game of Life?

A

Alive cells with 2 or 3 cells stay alive

27
Q

Cellular automata

What is the reproduction rule in the Game of Life?

A

Dead cells with exactly 3 neighbours come alive

28
Q

Cellular automata

What is the droplet rule?

A

A type of panic propagation.
- Normal individuals with 4+ panicky neighbours also panic.
- Panicky individuals stay panicked if 3+ neighbours are panicked.

29
Q

Cellular automata

What is a phase transition?

A

A phase transition is a transition of macroscopic properties of a collective system that occurs when its environmental or internal conditions are changed.

30
Q

Cellular automata

What are Stochastic cellular automata?

A

CA with probabilistic state-transition rules

31
Q

Cellular automata

What are Asynchronous cellular automata?

A

CA where the whole grid might not update at the same time

32
Q

Cellular automata

What are some Asynchronous updating mechanisms? (3)

A
  • Random updating
  • Sequential
  • State triggered
33
Q

Cellular automata

Are synchronous or asynchronous CA models deemed more robust and applicable to real-world problems

A

Asynchronous.

34
Q

Cellular automata

What are Turing Patterns?

A

A type of CA with update rules based on short-range activation and long-range inhibition. Cells in the immediate neighbourhood awakens the cell; cells further away kill the signal.

35
Q

Cellular automata

What are Waves in excitable media?

A

CA rule where the state of the cells is activated by some condition, and then the signal slowly decays. See the image.

36
Q

Cellular automata

What is a Host-pathogen CA model?

A

A model where cells can either be in one of several states, most notably empty, host or infected. Empty cells can spawn hosts. Infected hosts can infect other nearby hosts. Infected hosts die and become empty.

37
Q

Cellular automata

What is Epidemic-forest fire CA?

A

A model where cells can be (1) empty have or (2) contain trees. Trees can (3) catch fire or spread to other trees, and they can be (4) burned down.

38
Q

What is this an example of?

A

Turing patterns in practice.

39
Q

What is this an example of?

A

Waves in excitable media

40
Q

What is this an example of?

A

Phase transition