Additional Study

Question 1

Difference between 1D cA and 2D CA?

Answer 1

1. Grid structure
   
   • 1D CA: Consists of a single row of cells arranged in a line.
   • 2D CA: Consists of a grid or lattice of cells arranged in rows and columns.
     (1 mark)
2. Neighbourhood definition
   
   • 1D: Each cell typically interacts with its left and right neighbours (radius-1 neighbourhood).
   • 2D: Each cell interacts with neighbours in multiple directions — usually the von Neumann (4-neighbour) or Moore (8-neighbour) neighbourhood.
     (1 mark)
3. Rule complexity
   
   • 1D: Rules are simpler, often binary and based on a small number of neighbouring cells (e.g., Wolfram’s Rule 30).
   • 2D: Rules are more complex, involving larger neighbourhoods and multiple interaction patterns (e.g., Conway’s Game of Life).
     (1 mark)
4. Visual representation
   
   • 1D: Evolving over time forms a 2D pattern (space × time).
   • 2D: Evolving over time forms a 3D pattern (two spatial dimensions + time).
     (1 mark)
5. Behaviour and applications
   
   • 1D: Used mainly for theoretical exploration, pattern generation, and simple models of computation.
   • 2D: Used to model spatial phenomena such as diffusion, fire spread, epidemics, and ecological systems.
     (1 mark)
6. Example models
   
   • 1D: Wolfram’s elementary cellular automata.
   • 2D: Conway’s Game of Life or forest-fire models.
     (1 mark)

Question 2

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