Cellular automata and ultra-discrete Painlevé equations

B. Grammaticos*, Y. Ohta, A. Ramani, D. Takahashi, K. M. Tamizhmani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)


Starting from integrable cellular automata we present a novel form of Painlevé equations. These equations are discrete in both the independent variable and the dependent one. We show that they capture the essence of the behavior of the Painlevé equations, organize themselves into a coalescence cascade and possess special solutions. A necessary condition for the integrability of cellular automata is also presented. We conclude with a discussion of the notion of integrability of the cellular automata under examination.

Original languageEnglish
Pages (from-to)53-58
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number1-2
Publication statusPublished - 1997 Feb 10
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


Dive into the research topics of 'Cellular automata and ultra-discrete Painlevé equations'. Together they form a unique fingerprint.

Cite this