Regular Paperfolding Sequence

In mathematics the regular paperfolding sequence, also known as the dragon curve sequence, is an infinite automatic sequence of 0s and 1s defined as the limit of the following process:

1
1 1 0
1 1 0 1 1 0 0
1 1 0 1 1 0 0 1 1 1 0 0 1 0 0

At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous sequence. The sequence takes its name from the fact that it represents the sequence of left and right folds along a strip of paper that is folded repeatedly in half in the same direction. If each fold is then opened out to create right angled corner, the resulting shape approaches the dragon curve fractal. For instance the following curve is given by folding a strip four times to the right and then unfolding to give right angles, this gives the first 15 terms of the sequence when 1 represents a right turn and 0 represents a left turn.

Starting at n = 1, the first few terms of the regular paperfolding sequence are:

1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, ... (sequence A014577 in OEIS)

Read more about Regular Paperfolding Sequence:  Properties, Generating Function, Paperfolding Constant, General Paperfolding Sequence

Famous quotes containing the words regular and/or sequence:

    He hung out of the window a long while looking up and down the street. The world’s second metropolis. In the brick houses and the dingy lamplight and the voices of a group of boys kidding and quarreling on the steps of a house opposite, in the regular firm tread of a policeman, he felt a marching like soldiers, like a sidewheeler going up the Hudson under the Palisades, like an election parade, through long streets towards something tall white full of colonnades and stately. Metropolis.
    John Dos Passos (1896–1970)

    We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.
    —E.M. (Edward Morgan)