From the 1 of 7 linked papers with an AI index.
7 papers
Aperiodic tile sets from Sturmian lattices
Shigeki Akiyama, Tadahisa Hamada, Katsuki Ito
The paper presents an explicit algorithm that builds aperiodic tile sets using Sturmian words with quadratic irrational slopes, linking the construction to Sturmian lattices and bo…
Dynamical systems defined by polynomials with algebraic properties
Shigeki Akiyama, Xiang Gao, Teturo Kamae
Let (x_n; n\in Z) be a bisequence of elements x_n in the 1-dimensional torus R/Z, which is called a stream over R/Z. Let P(z)=a_k z^k+...+a_1 z+a_0 be a polynomial with integer coe…
Discretized Rotation with fixed initial points
Shigeki Akiyama, Bill Mance
We prove that if and , then the sequence defined by is periodic.
Sturmian lattices and Aperiodic tile sets
Shigeki Akiyama, Tadahisa Hamada, Katsuki Ito
We give an explicit algorithm to construct aperiodic tile sets based on Sturmian words of quadratic slopes. The method works for any quadratic irrational slope, and we can produce…
Delone sets associated with badly approximable triangles
Shigeki Akiyama, Emily R. Korfanty, Yanli Xu
We construct new Delone sets associated with badly approximable numbers which are expected to have rotationally invariant diffraction. We optimize the discrepancy of corresponding…
An alternative proof for an aperiodic monotile
Shigeki Akiyama, Yoshiaki Araki
We give an alternative simple proof that the monotile introduced by Smith, Myers, Kaplan and Goodman-Strass is aperiodic.