![]() ![]() 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). ![]()
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