2009/01/21 by Steven M. Kautz, James I. Lathrop, Kautz, Steven M. +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #Cellular Automata and Applications #DNA and Biological Computing #FOS: Computer and information sciences #Fractal and DNA sequence analysis #Other Computer Science (cs.OH) #cs.OH
paper · pdf · doi:10.48550/arxiv.0901.3189
arxiv created 2009/01/21 · openalex publication_date 2009/01/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.