Ultradiscrete Systems (Cellular Automata)

  • Tetsuji Tokihiro
Part of the Lecture Notes in Physics book series (LNP, volume 644)


Ultradiscretization is a limiting procedure which allows one to obtain a cellular automaton (CA) from continuous equations. Using this method, we can construct integrable CAs from integrable partial difference equations. In this course, we focus on a typical integrable CA, called a Box and Ball system (BBS), and review its peculiar features. Since a BBS is an ultradiscrete limit of the discrete KP equation and discrete Toda equation, we can obtain explicit solutions and conserved quantities for the BBS. Furthermore the BBS is also regarded as a limit (crystallization) of an integrable lattice model. Recent topics, and a periodic BBS in particular are also reviewed.


Cellular Automaton Soliton Solution Young Diagram Fundamental Cycle Boltzmann Weight 
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Authors and Affiliations

  • Tetsuji Tokihiro
    • 1
  1. 1.Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914Japan

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