section2.04

Mini-exercise: Solve a tri-diagonal system

Exercise (20 minutes)

This exercise will solve a tri-diagonal system of equations as described here: https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm

The accompanying template exercise.f90 has some further instructions, and some suggestions on how to test the result.

A solution to the problem appears as a template to the exercise in section3.03.

Alternative Exercise (20 minutes)

In this exercise you will create a simple implementation of Conway's Game of Life. Game of Life is a cellular automata model where an array of cells is updated based on simple rules about the values of each neighbouring cell.

Using the rules described here (also summarised below), create an array with an initial starting pattern, then write code to advance the initial pattern to the next iteration based on the rules above.

To get an idea for what you need to implement, experiment using this online version of the game: https://playgameoflife.com/

A template exercise_alternative.f90 is provided with some hints to get you started.

The trim() procedure is used in the template hints, we cover this later in more detail in section4.01, but to summarise for now, it is used to remove trailing blank characters, which may be useful in your implementation.

Staring pattern and first iteration

The starting board should look like this:

The first iteration should look like this:

Yellow squares represent live cells (set to 1) and grey squares represent dead cells (set to 0)

Hints

1. You only need a small NxN array to begin with, intialised with a simple pattern of 1's (live cells) and 0's (dead cells). You could design the starting pattern with the help of the online tool above to visulise it.

2. Your program might use the following steps:

   • Initialise a starting array with a basic pattern as shown in the diagram above.
   • Iterate over the array and inspect the neighbouring 8 cells, determining the number of live neighbours.
   • Update the current cell based on the Rules.
   • Once complete, print out the initial state of the board, then the next iteration.

3. If you complete the above, extend the implementation so that it iterates through multiple timesteps.

4. Consider how you might handle updating cells at the edges of your array (bounds checking)

A initial solution that prints the inital state and first iteration is provided in the relevant subfolder in the solutions folder.

Game of Life Rules

The Game of Life rules are summarised below:

Cell state	Sum of neighbouring 8 cells	New Cell state
1	0,1	0
1	4,5,6,7,8	0
1	2,3	1
0	3	1
0	0,1,2,4,5,6,7,8	0

ASCII art representation of initial and first iteration

Your program should produce something like this when run.

$ ./a.out 
 Initial Board Set-up:
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 First iteration of the GoL rules:
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