Lecture Notes in Computer Science Volume 2943, 2004, pp 91-107

Self-Assembled Circuit Patterns

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Self-assembly is a process in which basic units aggregate under attractive forces to form larger compound structures. Recent theoretical work has shown that pseudo-crystalline self-assembly can be algorithmic, in the sense that complex logic can be programmed into the growth process [26]. This theoretical work builds on the theory of two-dimensional tilings [8], using rigid square tiles called Wang tiles [24] for the basic units of self-assembly, and leads to Turing-universal models such as the Tile Assembly Model [28]. Using the Tile Assembly Model, we show how algorithmic self-assembly can be exploited for fabrication tasks such as constructing the patterns that define certain digital circuits, including demultiplexers, RAM arrays, pseudowavelet transforms, and Hadamard transforms. Since DNA self-assembly appears to be promising for implementing the arbitrary Wang tiles [30,13] needed for programming in the Tile Assembly Model, algorithmic self-assembly methods such as those presented in this paper may eventually become a viable method of arranging molecular electronic components [18], such as carbon nanotubes [10,1], into molecular-scale circuits.
This revised version was published in November 2004 and replaces the previous preliminary version.