These games will all be played on a square grid like a sheet of graph paper. Each game has a set of rules. The rules say when to fill in and when to erase squares from the grid. The decision to erase or fill in a square is always made by looking at the eight neighboring squares that surround a square and counting how many of them are filled in. The most famous game of the kind is the "Game of Life" invented by John Conway in the sixties. The rules say: Fill an empty square if exactly three of the neighboring squares are full. Empty a full square unless two or three of the neighboring squares are full. 
In the Life game, people often talk about live cells and dead cells rather than full squares and empty squares. The rules can then be restated as: A live cell with more than three neighbors dies of overcrowding. A live cell with less than two neighbors dies of loneliness. A dead cell with three neighbors enjoys ideal conditions so it becomes alive. 

Even though the rules don't talk about objects, lots of different objects emerge. There are "still lifes" where each cell in a structure has two or three neighbors. This makes the whole structure stable. There are "blinkers," structures that switch back and forth between two forms. Look closely at them and you'll see that they are just following the rules. There are also "gliders," structures that move across the screen. They move by reforming copies of themselves a little bit beside the originals. 
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Brian Silverman
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