2017/12/27 by Francis Oger, Oger, Francis
Computer Science · Engineering · Materials Science · Physics and Astronomy · #05B45 (52C20 #52C23) #Advanced Materials and Mechanics #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Quasicrystal Structures and Properties #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1712.09545
openalex publication_date 2017/12/27 · openalex created_date 2023/11/01 · openalex updated_date 2026/07/28
We consider n-folding triangular curves, or n-folding t-curves, obtained\nby folding n times a strip of paper in 3, each time possibly left then\nright or right then left, and unfolding it with \π /3 angles. An example is\nthe well known terdragon curve. They are self-avoiding like n-folding curves\nobtained by folding n times a strip of paper in two, each time possibly left\nor right, and unfolding it with \π /2 angles.\n We also consider complete folding t-curves, which are the curves without\nendpoint obtained as inductive limits of n-folding t-curves. We show that\neach of them can be extended into a unique covering of the plane by disjoint\nsuch curves, and this covering satisfies the local isomorphism property\nintroduced to investigate aperiodic tiling systems. Two coverings are locally\nisomorphic if and only if they are associated to the same sequence of foldings.\nEach class of locally isomorphic coverings contains exactly 2\ω \n(resp. 2\ω , 2 or 5, 0) isomorphism classes of coverings by 1\n(resp. 2, 3, \≥ 4) curves. These properties are partly similar to those\nof complete folding curves.\n