4 papers
Overlapping substitutions and tilings
Shigeki Akiyama, Yasushi Nagai, Shu-Qin Zhang
We generalize the notion of (geometric) substitution rule to obtain overlapping substitutions. Our motivating example is the substitution presented in Ziherl, Dotera and Bekku \cit…
Self-descriptive Sequences directed by two Periodic Sequences
Shigeki Akiyama, Damien Jamet, Irène Marcovici +1
In the present work, we exhibit a class of self-descriptive sequences that can be explicitly computed and whose frequencies are known. In particular, as a corollary of our main res…
Intersection the twin dragon with rational lines
Shigeki Akiyama, Paul Grosskopf, Benoît Loridant +1
The Knuth Twin Dragon is a compact subset of the plane with fractal boundary of Hausdorff dimension , . Although the intersection with…
Non-self-intersective dragon curves
Shigeki Akiyama, Yuichi Kamiya, Fan Wen
Let us fold a strip of paper many times in the same direction, and then unfold it to form a fixed angle at all creases. The resulting shape is called the Dragon curve with the…