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<p>Self-assembly refers to the process by which small, simple components mix and combine to form complex structures using only local interactions. Designed as a hybrid between tile assembly models and cellular automata, the <i>Tile Automata (TA) model</i> was recently introduced as a platform to help study connections between various models of self-assembly. However, in this paper we present a result in which we use TA to simulate arbitrary systems within the <i>amoebot model</i>, a theoretical model of programmable matter in which the individual components are relatively simple state machines that are able to sense the states of their neighbors and to move via series of expansions and contractions. We show that for every amoebot system, there is a TA system capable of simulating the local information transmission built into amoebot particles, and that the TA “macrotiles” used to simulate its particles are capable of simulating movement (via attachment and detachment operations) while maintaining the necessary properties of amoebot particle systems. The TA systems are able to utilize only the local interactions of state changes and binding and unbinding along tile edges, but are able to fully simulate the dynamics of these programmable matter systems. Since the signal-passing tile assembly model, a mathematical model of “active” DNA-based tile self-assembly, has been shown to be able to simulate the TA model, our result provides a bridge showing how DNA-based self-assembling tiles can simulate the behavior of the amoebot model of programmable matter.</p>

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Simulation of programmable matter systems using active tile-based self-assembly

  • 期刊论文

  • 发表日期：

    2025年6月5日

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  • John Calvin Alumbaugh,
  • Joshua J. Daymude,
  • Erik D. Demaine,
  • Matthew J. Patitz,
  • Andréa W. Richa

摘要

Self-assembly refers to the process by which small, simple components mix and combine to form complex structures using only local interactions. Designed as a hybrid between tile assembly models and cellular automata, the Tile Automata (TA) model was recently introduced as a platform to help study connections between various models of self-assembly. However, in this paper we present a result in which we use TA to simulate arbitrary systems within the amoebot model, a theoretical model of programmable matter in which the individual components are relatively simple state machines that are able to sense the states of their neighbors and to move via series of expansions and contractions. We show that for every amoebot system, there is a TA system capable of simulating the local information transmission built into amoebot particles, and that the TA “macrotiles” used to simulate its particles are capable of simulating movement (via attachment and detachment operations) while maintaining the necessary properties of amoebot particle systems. The TA systems are able to utilize only the local interactions of state changes and binding and unbinding along tile edges, but are able to fully simulate the dynamics of these programmable matter systems. Since the signal-passing tile assembly model, a mathematical model of “active” DNA-based tile self-assembly, has been shown to be able to simulate the TA model, our result provides a bridge showing how DNA-based self-assembling tiles can simulate the behavior of the amoebot model of programmable matter.