### Abstract

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.

Original language | English |
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Title of host publication | Self-Organizing Robots |

Pages | 59-75 |

Number of pages | 17 |

Edition | STAR |

DOIs | |

Publication status | Published - 2012 Apr 27 |

### Publication series

Name | Springer Tracts in Advanced Robotics |
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Number | STAR |

Volume | 77 |

ISSN (Print) | 1610-7438 |

ISSN (Electronic) | 1610-742X |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Artificial Intelligence

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## Cite this

Murata, S., & Kurokawa, H. (2012). Basics in mathematics and distributed algorithms. In

*Self-Organizing Robots*(STAR ed., pp. 59-75). (Springer Tracts in Advanced Robotics; Vol. 77, No. STAR). https://doi.org/10.1007/978-4-431-54055-7_4