From the biggest picture to the smallest interaction
Now you connect the midpoints of the sides to divide it into three triangles that are ½ as big. (There really are four, plus the original one, but it looks like three.)
Now you take each of the three, and you divide them. You have nine triangles, each the 1/4 the size of our original.
Do it again! Now you have 27 triangles, each 1/8 the size of the original. You can
keep on doing this, and the patterns are not the same, but they are similar, on a smaller and smaller scale.
This is one of the simplest illustrations of the concept of fractal geometry, which you may have heard of, and which has all sorts of useful applications in the real world. Some very simple rules (like “connect the midpoints of a triangle”) can result in some very complex and beautiful patterns.
(Don’t worry, this is not a TED talk, there’s a sermon in here somewhere.)