Corpus ID: 119316809

Seas of squares with sizes from a $\Pi^0_1$ set

  title={Seas of squares with sizes from a \$\Pi^0_1\$ set},
  author={L. Westrick},
  journal={arXiv: Dynamical Systems},
  • L. Westrick
  • Published 2016
  • Mathematics
  • arXiv: Dynamical Systems
  • For each $\Pi^0_1$ $S\subseteq \mathbb{N}$, let the $S$-square shift be the two-dimensional subshift on the alphabet $\{0,1\}$ whose elements consist of squares of 1s of various sizes on a background of 0s, where the side length of each square is in $S$. Similarly, let the distinct-square shift consist of seas of squares such that no two finite squares have the same size. Extending the self-similar Turing machine tiling construction of Durand, Romashchenko and Shen, we show that if $X$ is an $S… CONTINUE READING
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