Dragon curveLet us now generate an intricately complex curve known as the Dragon curve. We begin with a long strip of paper placed on the table and fold it at the middle of it in the same direction repeatedly as shown. That is, you do not turn over the folded paper strip at any stage of folding.
Of course, we assume the paper is so thin that folding it repeatedly at the middle will crease the paper strip exactly at the locations
Figure 5. Dragon curve
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, etc. Here, the number of flat paper strips increases by the doubling numbers, 2, 4, 8, 16, ... (see, Lesson 1). For the demonstration in figure 5, we maintain the right angle creases and a perfectly flat paper strip between the neighboring creases. Prog#3d lets you step through successive folding up to the 14th generation. At around the 12th generation folding, a faint impression of Chinese dragons begins to emerge, which then becomes more distinctive at the 13th and 14th generations. This had led its discover, J.E. Heighway, to coin the word, Dragon curve, for the meandering paper strip folding. 