07 April 2013

Summary

Wikipedia summarises the Game Of Life as:

The universe of the Game of Life is an infinite two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, alive or dead. Every cell interacts with its eight neighbours, which are the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:

``````Any live cell with fewer than two live neighbours dies, as if caused by under-population.
Any live cell with two or three live neighbours lives on to the next generation.
Any live cell with more than three live neighbours dies, as if by overcrowding.
Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
``````

Initial thoughts

Some elements of the game are quickly apparent:

• We need an intial state
• We need a way of moving on to the next generation of the system
• We need to return a representation of the current state of the grid.
• We can also be confident we need a way of determining the adjacent cells
• We need a concept of life and death.

When I first attempted this Kata I initially tried to create a state machine grid system, with cells having an IsAlive property. However, thinking this approach through a little further reveals it to be unworkable - we are supposed to be implementing an infinite grid, so we would in theory have to store an infinite number of dead cells. Hmmm… not a good plan. A better approach is to presume life by existence. If a cell exists, it is alive. This way, we only need to track live cells.

First Rule

Any live cell with fewer than two live neighbours dies, as if caused by under-population.

This is a reasonably simply rule, but forms the foundation on which we will build our game. We need to implement all of the items mentioned above before we can test this rule. We need to be able to iterate through current live cells, find out if they have fewer than two neightbours, and if so, kill them. This is the equivalent of removing them from our collection of cells.

Note: a gotcha here is to remember to exclude the current cell from this equation

Second Rule

Any live cell with two or three live neighbours lives on to the next generation.

This is very similar to the first rule… In fact, come to think of it, so is the third rule:

Third Rule

Any live cell with more than three live neighbours dies, as if by overcrowding.

If we combine these rules, we have a very simple check for the count of live neighbours; 2 or 3 live neighbours and the cell lives, any other amount and it dies.

``````var cellsThatSurvive = liveCells.Where(cell => this.GetLiveAdjacentCells(cell).Count() == 2 ||
``````

Fourth Rule

Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

Things start to get a bit trickier now. We now need a way to revive dead cells. We need to get the dead neightbours and see if they have exactly three live neightbours. We already have code in place to count the number of live neighbours, so we just need a way of getting dead neighbours. Something along the lines of:

``````var cellsThatRevive = liveCells.SelectMany(GetDeadAdjacentCells).Where(cell =>
``````

These two collections can then be joined together to produce the output:

``````liveCells = new HashSet<Cell>(cellsThatSurvive.Union(cellsThatRevive));
``````

This passes the following tests:

• CellDiesWithNoNeighbours()
• CellDiesWithOneNeighbour()
• CellLivesWithTwoNeighbours()
• CellLivesWithThreeNeighbours()
• CellDiesWithFourNeighbours()
• CellDiesWithFiveNeighbours()
• CellDoesNotReviveWithTwoLiveNeighbours()
• CellRevivesWithThreeLiveNeighbours()
• CellDoesNotReviveWithFourLiveNeighbours()

https://github.com/tomliversidge/kata.gameoflife/