## Hiroshima Mathematical Journal

### Paperfolding sequences, paperfolding curves and local isomorphism

Francis Oger

#### Abstract

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.

#### Article information

Source
Hiroshima Math. J., Volume 42, Number 1 (2012), 37-75.

Dates
First available in Project Euclid: 30 March 2012

https://projecteuclid.org/euclid.hmj/1333113006

Digital Object Identifier
doi:10.32917/hmj/1333113006

Mathematical Reviews number (MathSciNet)
MR2952072

Zentralblatt MATH identifier
1309.52009

#### Citation

Oger, Francis. Paperfolding sequences, paperfolding curves and local isomorphism. Hiroshima Math. J. 42 (2012), no. 1, 37--75. doi:10.32917/hmj/1333113006. https://projecteuclid.org/euclid.hmj/1333113006