Name
Abstract | ||
|---|---|---|
We discuss the self-assembly system of triangular tiles instead of square
tiles, in particular right triangular tiles and equilateral triangular tiles.
We show that the triangular tile assembly system, either deterministic or
non-deterministic, has the same power to the square tile assembly system in
computation, which is Turing universal. By providing counter-examples, we show
that the triangular tile assembly system and the square tile assembly system
are not comparable in general. More precisely, there exists square tile
assembly system S such that no triangular tile assembly system is a division of
S and produces the same shape; there exists triangular tile assembly system T
such that no square tile assembly system produces the same compatible shape
with border glues. We also discuss the assembly of triangles by triangular
tiles and obtain results similar to the assembly of squares, that is to
assemble a triangular of size O(N^2), the minimal number of tiles required is
in O(log N/log log N). |
Year | Venue | Keywords |
|---|---|---|
2010 | Clinical Orthopaedics and Related Research | self assembly,discrete mathematics |
DocType | Volume | Citations |
Journal | abs/1002.4 | 0 |
PageRank | References | Authors |
0.34 | 3 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lila Kari | 1 | 1123 | 124.45 |
| Shinnosuke Seki | 2 | 189 | 29.78 |
| Zhi Xu | 3 | 9 | 2.61 |