Self-assembly of the discrete Sierpinski carpet and related fractals
| dc.creator | Kautz, Steven M. | |
| dc.creator | Lathrop, James I. | |
| dc.date | 2009-01-21 | |
| dc.date.accessioned | 2026-07-07T12:32:29Z | |
| dc.date.available | 2026-07-07T12:32:29Z | |
| dc.description | It is well known that the discrete Sierpinski triangle can be defined as the nonzero residues modulo 2 of Pascal's triangle, and that from this definition one can easily construct a tileset with which the discrete Sierpinski triangle self-assembles in Winfree's tile assembly model. In this paper we introduce an infinite class of discrete self-similar fractals that are defined by the residues modulo a prime p of the entries in a two-dimensional matrix obtained from a simple recursive equation. We prove that every fractal in this class self-assembles using a uniformly constructed tileset. As a special case we show that the discrete Sierpinski carpet self-assembles using a set of 30 tiles. | |
| dc.identifier | https://arxiv.org/abs/0901.3189 | |
| dc.identifier | http://arxiv.org/abs/0901.3189 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216797 | |
| dc.subject | Other Computer Science | |
| dc.title | Self-assembly of the discrete Sierpinski carpet and related fractals | |
| dc.type | text |