Homework 1: The Game of Life (100 points)

Rules for the Game of Life

Life is really a simulation, not a game with players. It takes place on an unbounded
rectangular grid in which each cell can either be occupied by an organism or not.
Occupied cells are called alive; unoccupied cells are called dead. Which cells are
alive changes from generation to generation according to the number of neighbor-
ing cells that are alive, as follows:

1. The neighbors of a given cell are the eight cells that touch it vertically, horizontally or diagonally.
2. If a cell is alive but either has no neighboring cells alive or only one alive, then
in the next generation the cell dies of loneliness.
3. If a cell is alive and has four or more neighboring cells also alive, then in the
next generation the cell dies of overcrowding.
4. A living cell with either two or three living neighbors remains alive in the next
generation.
5. If a cell is dead, then in the next generation it will become alive if it has exactly
three neighboring cells, no more or fewer, that are already alive. All other dead
cells remain dead in the next generation.
6. All births and deaths take place at exactly the same time, so that dying cells
can help to give birth to another, but cannot prevent the death of others by
reducing overcrowding; nor can cells being born either preserve or kill cells
living in the previous generation.

A particular arrangement of living and dead cells in a grid is called a configuration.
The preceding rules explain how one configuration changes to another at each
generation.

Implement the "The Game of Life" in your programming language of choice.

Please try the following simple life configurations: