Paperfolding sequences, paperfolding curves and local isomorphism

Details Paperfolding sequences, paperfolding curves and local isomorphism Paperfolding sequences, paperfolding curves and local isomorphism

2008-06-06

arxiv.org/abs/0806.1210v4

Mathematics

Combinatorics

39 pages containing 9 figures; to be read in pdf; minor changes to improve the readability, especially concerning the figures

Scientific paper

For each integer n, an n-folding curve is obtained by folding n times a strip of paper in two, possibly up or down, and unfolding it with right angles. Generalizing the usual notion of infinite folding curve, we define complete folding curves as the curves without endpoint which are unions of increasing sequences of n-folding curves for n integer. We prove that there exists a standard way to extend any complete folding curve into a covering of the plane by disjoint such curves, which satisfies the local isomorphism property introduced to investigate aperiodic tiling systems. This covering contains at most six curves.

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