Mobile RAM and shape formation by programmable particles

Giuseppe Antonio Di Luna, Paola Flocchini, Nicola Santoro, Giovanni Viglietta, Yukiko Yamauchi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)


In the distributed model Amoebot of programmable matter, the computational entities, called particles, are anonymous finite-state machines that operate and move on a hexagonal tessellation of the plane. In this paper we show how a constant number of such weak particles can simulate a powerful Turing-complete entity that is able to move on the plane while computing. We then show an application of our tool to the classical Shape-Formation problem, providing a new and much more general distributed solution. Indeed, while the existing algorithms allow to form only shapes made of arrangements of segments and triangles, our algorithm allows the particles to form also more abstract and general connected shapes, including circles and spirals, as well as fractal objects of non-integer dimension. In lieu of the existing impossibility results based on the symmetry of the initial configuration of the particles, our result provides a complete characterization of the connected shapes that can be formed by an initially simply connected set of particles. Furthermore, in the case of non-connected target shapes, we give almost-matching necessary and sufficient conditions for their formability.

Original languageEnglish
Title of host publicationEuro-Par 2020
Subtitle of host publicationParallel Processing - 26th International Conference on Parallel and Distributed Computing, Proceedings
EditorsMaciej Malawski, Krzysztof Rzadca
Number of pages16
ISBN (Print)9783030576745
Publication statusPublished - 2020
Event26th International European Conference on Parallel and Distributed Computing, Euro-Par 2020 - Warsaw, Poland
Duration: Aug 24 2020Aug 28 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12247 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference26th International European Conference on Parallel and Distributed Computing, Euro-Par 2020

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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