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March 2012 Paperfolding sequences, paperfolding curves and local isomorphism
Francis Oger
Hiroshima Math. J. 42(1): 37-75 (March 2012). DOI: 10.32917/hmj/1333113006


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 $R^2$ 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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Francis Oger. "Paperfolding sequences, paperfolding curves and local isomorphism." Hiroshima Math. J. 42 (1) 37 - 75, March 2012.


Published: March 2012
First available in Project Euclid: 30 March 2012

zbMATH: 1309.52009
MathSciNet: MR2952072
Digital Object Identifier: 10.32917/hmj/1333113006

Primary: 05B45
Secondary: 52C20, 52C23

Rights: Copyright © 2012 Hiroshima University, Mathematics Program


Vol.42 • No. 1 • March 2012
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