Discrete Maths II - Simulations

Question 1

What are discrete simulations?

Answer 1

• Seek to model a physical process
• Using discrete data structures
  
  • Agent-based models
  • Random Walks
  • Cellular automata

Question 2

What is the basic Model of Discrete Simulations?

Answer 2

Question 3

What is the basic weighted model of a discrete simulation?

Answer 3

• Agent resides at A
• Can move to B or C
• Change of picking edge
  
  • Weight of edge/weight of all edges connected to agents location

Question 4

What is the Random Walk Algorithm?

Answer 4

Question 5

What are the applications of random walk algorithms?

Answer 5

Random walks can be applied to approximate a variety of phenomena

• NPC movement
• Fluctuation of share prices
• Brownian (molecule) motion

Question 6

What is cellular Automata?

Answer 6

• A cellular automaton is a form of discrete simulation.
• It is based on a grid of cells, each with a finite number of states (e.g., on or off).
• The transition to a new generation (or time step) is determined by a fixed rule.
• This fixed rule is typically dependent on the current state of a cell and the states of its neighboring cells.
• Often, the rule only considers adjacent cells for determining the state of a cell in the new generation.

Question 7

What is Conway’s Game of Life?

Answer 7

Example of a cellular automaton. In this game:

1. Any live cell with fewer than two live neighbours dies, as if caused by underpopulation.
2. Any live cell with two or three live neighbours lives on to the next generation.
3. Any live cell with more than three live neighbours dies, as if by overpopulation.
4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.