BSE August 2011, Computer Science
The Game of Life

The  Game of Life was described by the English mathematician John Conway. The game is not really a game. There are no players, and no winning or losing. All you need to do to play the game is create an initial configuration, and let the system evolve.

Rules 
The universe in the Game of Life is a two-dimensional grid of cells, each of which is in one of two possible states: live or dead.
Every cell interacts with its 8 neighbors,  which are the cells that are horizontally, vertically or diagonally adjacent. At each step in time, the following transitions occur:

1. Any live cell with fewer than two live neighbors dies (as if caused by under-population).
2. Any live cell with two or three live neighbors lives on to the next generation.
3. Any live cell with more than three live neighbors dies  (as if by overcrowding).
 4. Any dead cell with exactly three live neighbors becomes a live cell  (as if by reproduction).

Note:  the number of neighbors is always based on the cells before the rule was applied.
The initial pattern constitutes the seed of the system. 
The first generation is created by applying the above rules simultaneously to every cell in the seed.  Births and deaths occur simultaneously. The rules continue to be applied repeatedly to create further generations. 
A lot of interesting patterns in the Game of Life have been discovered along the years (some without the use of computers!).  The simplest patterns are the ``still lives'', the ``oscilators'' (toad, blinker), the ``spaceships'' (glider), the F-pentomino, etc. 

Here are some seed examples,  with live cells shown in black and dead cells shown in white.  
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What you have to do:  
For each of the seeds in the previous slides, apply the rules and show how it evolves over a couple of generations.  
For each generation, draw the grid representing the world.  Draw the initial grid (the seed), the grid of the  second generation (after applying the rules once), the grid of the third generation, and so on, until you see a pattern.