Lecture 02 - Complex systems Flashcards
What are the 5 parts that a complex system might have? (CLOSE)
- 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)
Cellular automata
What are automata?
a theoretical machine that changes its internal state based on inputs and its previous state
Cellular automata
What are cellular automata (CA)?
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
Cellular automata
Who invented cellular automata (CA)?
John von Neumann
Cellular automata
What is the definition of cellular automata (CA)? (5 things)
- 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
Cellular automata
What is a CA’s cell neighbourhood?
The cells close to it (depending on its neighbourhood radius).
Cellular automata
What is a state transition function? (CA)
The function that updates a single cell’s state during a time step update.
Cellular automata
What’s the difference between a von Neumann and a Moore neighbourhood?
(See image)
Cellular automata
What are these kinds of neighbourhoods called?
Left: Von Neumann neighbourhood
Right: Moore neighbourhood
Cellular automata
What does it mean when a cell is quiescent?
It remains in the same state if all neighbours are quiescent
Cellular automata
What does it mean when a cell is active?
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.
Cellular automata
In CA, what do boundary conditions belong to?
They are properties of the CA grid.
Cellular automata
What are the four CA boundary conditions called?
- No Boundaries
- Periodic
- Cut-off
- Fixed
Cellular automata
What are the “No Boundaries” Boundary conditions?
infinite space filled with quiescent cells
Cellular automata
What are the “Periodic boundaries” Boundary conditions?
wrap around
Cellular automata
What are the “Cut-off boundaries” Boundary conditions?
no neighbours at the edge
Cellular automata
What are the “Fixed boundaries” Boundary conditions?
fixed state at the edge
Cellular automata
(Double check answer) What is a Totalistic CA?
Totalistic CA is CA where a cell’s transition depends only on the neighbourhood, e.g. sum of neighbours.
Cellular automata
What is the Majority rule? (binary CA rules)
Next state is the majority in the neighborhood
Cellular automata
What is the behaviour of Majority rule? (binary CA rules)
Self-organizes into geographically separated patches
Cellular automata
What is another name for the Parity rule? (binary CA rules)
The XOR rule
Cellular automata
What is the behaviour of the Parity rule? (binary CA rules)
Any pattern in the initial configuration replicates and propagates
Cellular automata
What are the four rules for Game of Life called?
- Happiness
- Overcrowding
- Loneliness
- Reproduction
Cellular automata
What is the loneliness rule in the Game of Life?
Alive cells with fewer than 2 alive neighbours die
