Model for self-replicating, self-assembling electric circuits with self-controlled growth

Abstract

Tile self-assembly models have proved to be important theoretical tools for studying nanoscale manufacturing techniques, and have provided insight into the computational capabilities of systems inspired by molecular biology. A tile assembly model (rcTAM), whose tiles are composed of simple electric circuit components, exhibits three important properties akin to those found in living organisms. First, it grows from a seed tile by self-assembly of component tiles. Second, it autonomously stops growth when a maximum size is reached, as determined by parameters associated with the tiles. Third, when the circuit assembly has reached the limit of its growth, it generates an identical copy of the original seed, which then will grow to replicate a copy itself. The size of the assembled circuit is controlled by values of the circuit components (voltage sources, resistors), and a threshold voltage for tile attachment. Since every new tile attachment instantly changes the circuit properties, such as voltage drops and currents across resistors, as well as equivalent resistances, the model exhibits instantaneous distant communication and cooperation between components, as well as dynamic behavior. Proofs are given for a bound on growth, the self-replicating property, and possible aging phenomena that produce a stable circuit population. The model might have application to electrochemical growth processes at the nanoscale, and provides insight into self-replicating systems that are not necessarily composed of organic materials. In addition, it models certain features of bioelectric networks that contribute to pattern formation in collections of cells.

Publication Title

Physical Review Research

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