Periodic 3

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The repeating fundamental cell on the left is a hexagon. It contains 6 tiles, or motifs, and can go on tiling forever in a periodic way, up, down, left, and right. It's "periodic" because wherever you look on the page, you'll see that repeating fundamental cell, and t will always be the same size. Because the one on the right is not periodic, it has no fundamental cell that can be repeated. We can't call the line-ups of tiles along its sides "repeating fundamental cells" because the number of tiles in each line changes. We can write a formula to calculate how many cat heads will be in each line, but that's a variable, not a constant. The spiral can go on forever, but will never become periodic. You can see more of both types in the Galleries.

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