Fortune Teller Christmas Tree

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You can assemble a simple Christmas tree from multiple Fortune Tellers (which you probably already know how to fold). Each Fortune Teller is smaller than the previous level. A good scaling factor seems to be √2: it results in a tree with nice proportions and can be easily constructed if you start with an A4 sheet. Divide the sheet in two, and cut a square from one half. Use it to fold a Fortune Teller, and proceed with dividing and folding the other half. You can continue until the pieces are so small the smallest one looks almost like a sharp tip on the tree, or use the last sheet to improvise some neater pinnacle. This cutting and folding sequence can be used as a nice demonstration of the A-series sheets’ (also known as Silver Rectangle) properties, namely that cutting it in half produces a sheet with identical proportions.

The units are not connected in any other way than just by gravity, so the tree is not particularly stable. Looking at the tree from the top, you can see its fractal nature with the concentric pieces getting smaller and smaller. I think this design is quite elegant, even though I’m not completely satisfied with how I designed the tip of the tree.