Pictures worth a thousand tiles, a geometrical programming language for self-assembly

Abstract

International audienceWe present a novel way to design self-assembling systems using a notion of signal (or ray) akin to what is used in analyzing the behavior of cellular automata. This allows purely geometrical constructions, with a smaller specification and easier analysis. We show how to design a system of signals for a given set of shapes, and how to transform these signals into a set of tiles which self-assemble into the desired shapes. We show how to use this technique on three examples : squares (with optimal assembly time and a small number of tiles), general polygons, and a quasi periodic pattern : Robinson tiling

Hybrid intelligence aspects of programming in *AIDA algorithmic pictures

“…The authors point that the fundamental difference between diagrammatic and sentential representations is that the diagrammatic representation preserves explicitly the information about the topological and geometrical relations among the component of the problem, while the sentential representation does not. In addition, we would like to mention approaches related to analogical representations of programs (including a semiotic analysis of comics) [16], selfassembling tilings (for the creation of the desired shapes) [17], various types of information resources annotations [18,19], and the long-term activity of researchers in Certec (Sweden) [20] (where the use of pictures as language for people with disabilities is promoted).…”

A Domain-Specific Language for Programming in the Tile Assembly Model

“…This notion of independent signals is modeled already in other DSLs for the aTAM [1] and for similar systems such as cellular automata [3]. The join operation, however, makes sense in the aTAM but not in a system such as a cellular automaton, where each cell contains the same transition function(s).…”

Toward a molecular programming language for algorithmic self-assembly

“…This notion of independent signals is modeled already in other DSLs for the aTAM [11] and for similar systems such as cellular automata [14]. The join operation, however, makes sense in the aTAM but not in a system such as a cellular automaton, where each cell contains the same transition function(s).…”

“…Similarly, many different tile types, with different actual signal values, generated from the same tile template, may be placed during the growth of an assembly. Another difference between our language and that of [11] is that our language appears to be more general; rather than being geared specifically toward the creation of geometric shapes, our language is more low-level, but also more general. 1 Additionally, [49] presents a DSL which provides a higher level framework for the modeling of various selfassembling systems, while the focus of our DSL on the aTAM creates a more powerful platform for the development of complex tile assembly systems.…”