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T2 mosaic

Figure 1.9: The plane tiled by T2 triangles. Left: alpha phase, in which the triangles are stacked diagonally. Right: beta phase, in which they are stacked in columns.
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The next larger triangles, T2, can cover the plane in two different ways. One, which could be designated the alpha phase, strings the tiles out along diagonals, as shown in the left mosaic of Figure 1.9. The other, similar to the T1 mosaic, arranges the T2 tiles in columns, for which there is only one way to avoid unwanted sequences of three ones in a row. It constitutes the beta phase, shown in the right mosaic of the same figure.

The density of the alpha phase is $5/8$ or 62.5%, of the beta phase $6/9$ or 67%. In spite of the more favorable densities, neither mosaic is ever a predominant feature of evolutions from random initial configurations.

Jose Manuel Gomez Soto 2002-01-31