Basics in Mathematics and Distributed Algorithms

  • Satoshi Murata
  • Haruhisa Kurokawa
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 77)


In this chapter, we study briefly the mathematical foundations for building self-organizing mechanical systems. First, we discuss diffusion dynamics in a physical continuum, and then introduce reaction-diffusion systems that generate spatial patterns, and cellular automaton models which behave like those continuous systems in discrete state, space and time. Since the actual hardware realization of self-organizing mechanical systems often utilizes digital control and communication, some typical problems with such distributed information systems will be discussed.


Span Tree Cellular Automaton Reaction Term Leader Election Turing Pattern 
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Copyright information

© Haruhisa Kurokawa, Satoshi Murata 2012

Authors and Affiliations

  1. 1.Department of Bioengineering and Robotic Graduate School of EngineeringTohoku UniversitySendaiJapan
  2. 2.Intelligent Systems Institute Field Robotics Research GroupNational Institute of Advanced Science and Technology (AIST)TsukubaJapan

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