TY - CHAP

T1 - Basics in mathematics and distributed algorithms

AU - Murata, Satoshi

AU - Kurokawa, Haruhisa

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84860202308&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860202308&partnerID=8YFLogxK

U2 - 10.1007/978-4-431-54055-7_4

DO - 10.1007/978-4-431-54055-7_4

M3 - Chapter

AN - SCOPUS:84860202308

SN - 9784431540540

T3 - Springer Tracts in Advanced Robotics

SP - 59

EP - 75

BT - Self-Organizing Robots

ER -