An Exponentially Growing Nubot System Without State Changes

Chun-Ying Hou, Ho-Lin Chen

Abstract: Self-assembly is the process in which simple units assemble into complex structures without explicit external control. The nubot model was proposed to describe self-assembly systems involving active components capable of changing internal states and moving relative to each other. A major difference between the nubot model and many previous self-assembly models is its ability to perform exponential growth. Several previous works focused on restricting the nubot model while preserving exponential growth. In this work, we construct a nubot system which performs exponential growth without any state changes. All nubots stay in fixed internal states throughout the growth process. This construction not only improves the previous optimal construction, but also demonstrates new trade-offs between different types of rules in the nubot system.