Geometric Computations by Broadcasting Automata on the Integer Grid

  • Russell Martin
  • Thomas Nickson
  • Igor Potapov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6714)


In this paper we introduce and apply a novel approach for self-organization, partitioning and pattern formation on the non-oriented grid environment. The method is based on the generation of nodal patterns in the environment via sequences of discrete waves. The power of the primitives is illustrated by giving solutions to two geometric problems using the broadcast automata model arranged in an integer grid (a square lattice) formation. In particular we show linear time algorithms for: the problem of finding the centre of a digital disk starting from any point on the border of the disc and the problem of electing a set of automata that form the inscribed square of such a digital disk.


Geometric Computation Nodal Line Constant Delay Discrete Time Step Transmission Radius 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alderighi, S., Mazzei, T.: Broadcast Automata: a Parallel Scalable Architecture for Prototypal Embedded Processors for Space Applications. HICSS (5), 208–217 (1997)Google Scholar
  2. 2.
    Czyzowicz, J., Gąsieniec, L., Pelc, A.: Gathering Few Fat Robots in the Plane. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 350–364. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Peleg, D., Efrima, A.: Distributed algorithms for partitioning a swarm of autonomous mobile robots. Theoretical Computer Science 410(14), 1355–1368 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Hendriks, M.: Model Checking the Time to Reach Agreement. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 98–111. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Lee, G., Chong, N.: A geometric approach to deploying robot swarms. Annals of Mathematics and Artificial Intelligence, 257–280 (2008)Google Scholar
  6. 6.
    Kari, J.: Theory of cellular automata: a survey. Theor. Comput. Sci. 334 (2005)Google Scholar
  7. 7.
    Standing Waves (January 2010),

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Russell Martin
    • 1
  • Thomas Nickson
    • 1
  • Igor Potapov
    • 1
  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolU.K.

Personalised recommendations