DNA Tiles, Wang Tiles and Combinators
نویسندگان
چکیده
In this paper we explore the relation between Wang Tiles and Schonfinkel Combinators in order to investigate Functional Combinators as an programming language for Self-assembly and DNA computing. We show: How any combinatorial program can be expressed in terms of Wang Tiles, and again, how any computation of the program fits into a grid of tiles of a suitable finite, tile set, and finally, how a program for Self-assembly DNA computing can be obtained. The result is a general methodology that, given any computable function, allows to define a Self-assembly program that can be used to construct the computations of the function
منابع مشابه
Programming Self-Assembly of DNA Tiles
SKI is a Turing complete, language for programming in the aTAM model. A compilation technique provides a mapping from SKI into finite sets of DNA Tiles that self-assemble in the aTAM model. Though such sets are always finite, the number of Tiles may be relevant, the construction of the Tiles may be heavy and the self-assembly can produce wrong molecular growth. In this paper we discuss the cons...
متن کاملSelf-assembly of fully addressable DNA nanostructures from double crossover tiles
DNA origami and single-stranded tile (SST) are two proven approaches to self-assemble finite-size complex DNA nanostructures. The construction elements appeared in structures from these two methods can also be found in multi-stranded DNA tiles such as double crossover tiles. Here we report the design and observation of four types of finite-size lattices with four different double crossover tile...
متن کاملWang Tiles for Image and Texture Generation
This paper discusses the use of Wang Tiles for image and texture generation as originally presented in Cohen et al. , 2003. Creating large expanses of nonperiodic texture, point distributions or geometry can be efficiently done at runtime by constructing a tiling of the plane using a small set of Wang tiles. Wang Tiles are squares whose edges are each assigned a color. The method involves filli...
متن کاملAperiodic Sets of Square Tiles with Colored Corners
In this paper we formalize the concept of square tiles with colored corners, a new kind of tiles closely related to Wang tiles. We construct aperiodic sets of square tiles with colored corners and several new aperiodic sets of Wang tiles using isomorphisms between tilings. The smallest aperiodic set of square tiles with colored corners we have created consists of 44 tiles over 6 colors.
متن کاملProgrammable Assembly at the Molecular Scale: Self-Assembly of DNA Lattices (Invited Paper)
DNA self-assembly is a methodology for the construction of molecular scale structures. In this method, arti cially synthesized single stranded DNA self-assemble into DNA crossover molecules (tiles). These DNA tiles have sticky ends that preferentially match the sticky ends of certain other DNA tiles, facilitating the further assembly into tiling lattices. DNA self-assembly can, using only a sma...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Fundam. Inform.
دوره 133 شماره
صفحات -
تاریخ انتشار 2013