Non-intersectivity of paperfolding dragon curves and of curves generated by automatic sequences. (English) Zbl 1448.11063
In this paper, the authors discuss the intersectivity of dragon curves obtained by unfolding a regularly folded strip of paper at an angle different from 90 degrees. They survey the (non-)intersectivity of curves associated with sequences taking their values in a finite set, in particular in the case of morphic or automatic sequences. They list papers about fractal curves, plane-filling curves, self-affine curves, or tilings, curves obtained by drawing sums of exponentials. They also present a result from the unpublished thesis of R. Albers (Bremen): The paperfolding curve is intersective if the unfolding angle is strictly between 90 and 95.126 degrees.
Reviewer: Michel Rigo (Liège)
Software:
OEISOnline Encyclopedia of Integer Sequences:
Digits of the infinite Fibonacci word A003849 grouped 2 by 2 and interpreted as a binary value.References:
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