Marcus Pivato 2002 Nonlinearity 15 1781 doi:10.1088/0951-7715/15/6/305
Marcus Pivato
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If
is a discrete Abelian group and
a finite set, then a cellular automaton (CA) is a continuous map
:![]()
→![]()
that commutes with all
-shifts. If
:
→
, then, for any a![]()
![]()
, we define Σ
(a) = ∑x![]()
![]()
(ax) (if finite);
is conserved by
if Σ
is constant under the action of
.
We characterize such conservation laws in several ways, deriving both theoretical consequences and practical tests, and provide a method for constructing all one-dimensional CA exhibiting a given conservation law.
20K45 Topological methods (See also 22A05, 22B05)
37E05 Maps of the interval (piecewise continuous, continuous, smooth)
Issue 6 (November 2002)
Received 5 November 2001, in final form 17 June 2002
Published 16 September 2002
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