Lecture 2 - Cellular Systems Flashcards
Intended learning outcomes:
1) Understand when we should/can apply CA.
2) Implement CA rules in a simulator to visualise the outcome.
3) Design your own CA rules (highlighting the neighbourhood used).
4) List the limitation of CAs with respect to other modelling tools.
5) Know how to qualitatively classify CAs (uniform final state, simple stable or periodic final state, chaotic, complex…)
6) Explain what the universality of CAs mean
n/a
When modelling a cellular system, what four concepts need to be considered?
- Cell and cellular space
- Neighbourhood (local interaction)
- Cell state
- Transition rule
What is a neighbourhood?
The set of cells that can directly influence a given cell
In homogeneous cellular models, what is special about the neighbourhood?
The neighbourhood is the same shape for all cells
Name the following neighbourhoods (Where 🔶 is the cell we’re looking at):
a) ◻◻◻◻◻ ◻◼◼◼◻ ◻◼🔶◼◻ ◻◼◼◼◻ ◻◻◻◻◻ b) ◻◻◻◻◻ ◻◻◼◻◻ ◻◼🔶◼◻ ◻◻◼◻◻ ◻◻◻◻◻
a) Moore
b) von Neumann
The ________ specifies the new state corresponding to each possible configuration of states of the cells in the neighbourhood.
a) cellular space
b) transition rule
c) cellular automaton
d) abstraction
b) transition rule
The transition rule can be represented as a
transition table.
In a 1D CA, if we have 2 possible states and we are looking the neighbour either side (3 neighbours, including the focal cell), how many rules would this table contain?
k states and n cells in the neighbourhood results in k^n rules.
2^3 = 8
Name four common boundary conditions used in CA.
1) Assigned
2) Periodic
3) Adiabatic
4) Reflection
There are 7 steps to consider when running a Cellular Automaton. 4 of these steps are listed below. What are the three missing steps?
- Assign the geometry of the CA space
- Assign the geometry of the neighbourhood
- Define the set of states of the cells
- Assign the transition rule
- Assign the boundary conditions
- Assign the initial conditions of the CA
- Repeatedly update all the cells of the CA, until some
stopping condition is met (for example, a preassigned
number of steps is attained, or the CA is in a
quiescent state, or cycles in a loop,…).
What special rules can be used when designing a CA so that the total number of entries of a transition table are decreased? What do these rules mean?
- Totalistic. The new value of the state depends only on the sum of the values of the states of the cells in the neighbourhood
- Outer totalistic. Similar to totalistic, but also depends on the value of the state of the updated cell. (Game of Life uses this rule if you need an example [Slide 39/62] )
There are four qualitative behavioural classes, what are they?
1) Uniform final state
2) Simple stable or periodic final state
3) Chaotic, random, nonperiodic patterns
4) Complex, localized, propagating structures
(Make sure you know how to classify behaviours by looking at the final iterations of a CA!!)
Game of Life is capable of universal computation. What does this mean?
That it can emulate any computing machine
Game of Life is a very simple CA and yet can produce highly nontrivial behaviours that cannot be predicted by looking at the initial state or transition rule. We must run it. What is this called?
Computational irreducibility
von Neumann created some bare complex self replicating machine. simpler self replicating machines have since been designed and implemented. give a couple examples.
1984 Langton’s Loop (Artificial Life)
Self replicating robots (Cornell Uni)
Some wavey evolutionary robot (Cambridge)
What else can CA be used for? Give examples?
Computation. can be used as input-output devices. For example R132 computes the remainder of any initial value after division by 2.
Wireworld computer is a very complex system that finds prime numbers using logic gates and shit.
Maze solver. (imitates slime mould in biology).
opinion clustering
