Self-assembly of generative heterogeneous electric circuits.

An abstract model of electric circuit self-assembly that is amenable to exact analysis has been proposed in previous works in the circuit tile assembly model (cTAM) to understand self-assembled and self-controlled growth as emergent phenomena that are capable of complex behaviors, like self-replication. In the cTAMs, a voltage source represents a finite supply of energy that drives growth by attachment of a single circuit tile type until it is unable to overcome randomizing factors in the environment, represented by a threshold of hybridization at tip voltages. Here, the cTAM is extended to allow attachment of copies of any tile from a predetermined finite heterogeneous set of tile types, which may include resistors, inductances and/or capacitors. The system of circuits is fully solved analytically by novel methods and exact properties of the grown terminal circuits are established for size and response. These circuit models have found a number of applications in areas such as transmission lines, passive filters, topological insulators, bioelectric networks and even, quantum computation, so these results may apply to many other areas.