Tomonori Watanabe 2002 J. Phys. A: Math. Gen. 35 305 doi:10.1088/0305-4470/35/2/310
Tomonori Watanabe
Show affiliationsFollowing the proposal of a filtration technique by Nobe, Satsuma and Tokihiro, we concretely construct partial difference equations, which preserve any time evolution patterns of cellular automaton (CA) stably by the filtration technique. We illustrate how to develop a method of filtration for applying to the typical two spatial dimensional CA rule—the game of life—and verify that the filtration method provides the stable difference equation associated with the CA, compared with the inverse ultradiscretization. Besides, in order to discuss whether the filtration technique can lead one to partial differential equations from CA rules, we show a derivation of the Burgers equation from Rule 184 CA via the discrete Burgers equation constructed by the filtration method as an example.
39Axx Difference equations (For dynamical systems, see 37-XX)
Issue 2 (18 January 2002)
Received 5 June 2001, in final form 19 October 2001
Published 4 January 2002
Tomonori Watanabe 2002 J. Phys. A: Math. Gen. 35 305
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