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Replication of Arbitrary Hole-Free Shapes via Self-assembly with Signal-Passing Tiles

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Abstract

In this paper, we investigate the abilities of systems of self-assembling tiles which can each pass a constant number of signals to their immediate neighbors to create replicas of input shapes. Namely, we work within the Signal-passing Tile Assembly Model (STAM), and we provide a universal STAM tile set which is capable of creating unbounded numbers of assemblies of shapes identical to those of input assemblies. The shapes of the input assemblies can be arbitrary 2-dimensional hole-free shapes. This improves previous shape replication results in self-assembly that required models in which multiple assembly stages and/or bins were required, and the shapes which could be replicated were more constrained, as well as a previous version of this result that required input shapes to be represented at scale factor 2.

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Authors and Affiliations

  1. Department of Computer Science and Computer Engineering, University of Arkansas, Fayetteville, AR, USA

    Andrew Alseth & Matthew J. Patitz

  2. Department of Computer, Information, and Data Sciences, University of Wisconsin-River Falls, River Falls, WI, USA

    Jacob Hendricks

  3. Hamilton Institute and Department of Computer Science, Maynooth University, Maynooth, Ireland

    Trent A. Rogers

Authors
  1. Andrew Alseth
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  2. Jacob Hendricks
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  3. Matthew J. Patitz
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  4. Trent A. Rogers
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Correspondence to Andrew Alseth.

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This author’s work was supported in part by National Science Foundation Grant CAREER-1553166

This author’s research was supported in part by National Science Foundation grants CCF-1422152 and CAREER-1553166

Research supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 772766, Active-DNA project), and Science Foundation Ireland (SFI) under Grant number 15/ERCS/5746.

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Alseth, A., Hendricks, J., Patitz, M.J. et al. Replication of Arbitrary Hole-Free Shapes via Self-assembly with Signal-Passing Tiles. New Gener. Comput. 40, 553–601 (2022). https://doi.org/10.1007/s00354-022-00181-3

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  • DOI: https://doi.org/10.1007/s00354-022-00181-3

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