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In mathematics the regular paperfolding sequence, also known as the dragon curve sequence, is an infinite sequence of 0s and 1s. It is obtained from the repeating partial sequence
by filling in the question marks by another copy of the whole sequence. The first few terms of the resulting sequence are:
If a strip of paper is folded repeatedly in half in the same direction, i {\displaystyle i} times, it will get 2 i − 1 {\displaystyle 2^{i}-1} folds, whose direction is given by the pattern of 0's and 1's in the first 2 i − 1 {\displaystyle 2^{i}-1} terms of the regular paperfolding sequence. Opening out each fold to create a right-angled corner produces a sequence of polygonal chains that approaches the dragon curve fractal: