Binary sequences | Paper folding
Regular paperfolding sequence
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 1, ?, 0, ?, 1, ?, 0, ?, 1, ?, 0, ?, ... by filling in the question marks by another copy of the whole sequence. The first few terms of the resulting sequence are: 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, ... (sequence in the OEIS) If a strip of paper is folded repeatedly in half in the same direction, times, it will get folds, whose direction (left or right) is given by the pattern of 0's and 1's in the first terms of the regular paperfolding sequence. Opening out each fold to create a right-angled corner (or, equivalently, making a sequence of left and right turns through a regular grid, following the pattern of the paperfolding sequence) produces a sequence of polygonal chains that approaches the dragon curve fractal: (Wikipedia).
