Game of Life

the rules
The Game of Life was invented by John Horton Conway. [br]It is played on a board divided into squares—like a large piece of graph paper. [br]One can mark squares by placing x’s on some of the squares or by colouring the squares. These are the “people” in your population. [br]Two people (squares) are “neighbours” if they share either an edge or a corner.[br]Thus each square has eight neighbours—four to the left and right or above and below, and four diagonal.[br]The rules of the game are these: [br]1. If three people are neighbours to the same empty square, then they produce an offspring (another person) in that square [br]2. if some person has four or more neighbors, then it dies of overcrowding[br]3. If some person has one or fewer neighbors, then it dies of loneliness.
Explore the rules of the game in following applet.[br]You can show or hide the number of neighbours of each cell to undestand the evolutions.[br]In the applet a starts with a particular population (configuration), but at any time you can add or exclude cells by clicking on them.
the aim
Given any population configuration, all three rules are applied instantly to produce the next "generation" (configuration).[br]Now you can investigate the evolutions of populations:[br]Are there initial populations that will remain stable (don't change)?[br]Are there initial populations that are periodic (continuously shift between two confugurations)?[br]Are there initial populations that will die out quickly—or immediately? [br]Are there initial populations that will keep reproducing and become ever larger without bound?[br]Are there initial populations that will keep migrating over the board?[br]...

triomino 1

How does following triomino behaves?[br]Check the behaviour and look to the number of steps.
What's the evolution of the population?

tetramino 1

How does following tetramino behaves?[br]Check the behaviour and look to the number of steps.
How does the population behaves?

still lifes

Some populations are called still lifes because they're stable already from their initial configuration.[br]The square, the boat, the loaf, and the ship are some of them.[br]Showing the number of neighbours, you can examine in the applet why they're stable. Click on cells to colour or to uncolour them.[br]You can find more still lifes on the [url=]Conway-wiki[/url].
Other still live patterns


On [url=]simulation[/url] you can experiment with Conway's Game of Life on a larger board than the 6 x 6 squares of the GeoGeobra applets in this book. You can select some built-in configurations, like the Glider gun, a spaceship or an exploder.
screenshot of the simulation board:
This is just a non-active screenshot of the simulation. Click on the link above to really work with it.