The students should use the computer programs to view the evolution of this pattern and see how/where it becomes stable.

The class of patterns which start off small but take a very long time to become periodic and predictable are called Methuselahs. The F-pentomino stabilizes (meaning future iterations are easy to predict) after 1,103 iterations. In fact, it doesn't stabilize until generation 1103. A glider will keep on moving forever across the plane.Īnother pattern similar to the glider is called the 'lightweight space ship.' It too slowly and steadily moves across the grid.Įarly on (without the use of computers), Conway found that the F-pentomino (or R-pentomino) did not evolve into a stable pattern after a few iterations. The following pattern is called a 'glider.' The students should follow its evolution on the game board to see that the pattern repeats every 4 generations, but translated up and to the left one square. Here are some tetromino patterns (NOTE: The students can do maybe one or two of these on the game board and the rest on the computer): Some possible triomino patterns (and their evolution) to check: They should verify that any single living cell or any pair of living cells will die during the next iteration. Using the provided game board(s) and rules as outline above, the students can investigate the evolution of the simplest patterns. Settling into a stable configuration that remains unchanged thereafter, or entering an oscillating phase in which they repeat an endless cycle of two or more periods.Fading away completely (from overcrowding or from becoming too sparse).There should be simple initial patterns that grow and change for a considerable period of time before coming to an end in the following possible ways:.There should be initial patterns that apparently do grow without limit.There should be no initial pattern for which there is a simple proof that the population can grow without limit. Conway carefully examined various rule combinations according to the following three criteria: The rules above are very close to the boundary between these two regions of rules, and knowing what we know about other chaotic systems, you might expect to find the most complex and interesting patterns at this boundary, where the opposing forces of runaway expansion and death carefully balance each other.

Some of these variations cause the populations to quickly die out, and others expand without limit to fill up the entire universe, or some large portion thereof. Conway tried many of these different variants before settling on these specific rules. There are, of course, as many variations to these rules as there are different combinations of numbers to use for determining when cells live or die.

If the cell is dead, then it springs to life only in the case that it has 3 live neighbors.

If the cell is alive, then it stays alive if it has either 2 or 3 live neighbors.

For each generation of the game, a cell's status in the next generation is determined by a set of rules. Afterwards, the rules are iteratively applied to create future generations. The second generation evolves from applying the rules simultaneously to every cell on the game board, i.e. The initial pattern is the first generation. Neighbors of a cell are cells that touch that cell, either horizontal, vertical, or diagonal from that cell. The status of each cell changes each turn of the game (also called a generation) depending on the statuses of that cell's 8 neighbors.

The Game of Life (an example of a cellular automaton) is played on an infinite two-dimensional rectangular grid of cells.

The game of life