Only this time the angle between them is 180 degrees. Its two segments are also identical, and also arranged like the hands on an old style clock face. Its two segments are identical, and are joined like the hands on an old-fashioned clock-face, so that one is just rotated in relation to the other. When we isolate this fundamental domain, to the right, note next that we can snip its edge into two pairs of segments, one blue, one red. The rich yellow shape is the so-called fundamental domain out of which the entire pattern is made. Notice that the rosette it’s part of, with the paler infill, is made just by repeating the rich yellow shape at different orientations. Start from the shape with a rich yellow infill in the pattern on the left. There are a whole set of recipes, but to get an idea of how they work, take a look at just one. To make cells that tessellate, you have to follow a recipe. If you try to make a pattern like that out of any old shape, you will either end up with gaps or overlaps: In a tessellation, the cells can have wiggly edges, but still fit together like jig-saw pieces. However tiles are usually geometric shapes – rectangles or squares as a rule, though triangles or hexagons would be possible too. An obvious example would be tiles on a wall. Note added in March 2011! If you’re new to tessellations, before tackling this post, first watch my later post with an animation of how tessellations work.Īny regular pattern consists of identical areas, which repeat without overlaps or gaps.
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