“Problem 9. What is the correspondence between cellular automata and continuous systems?”

— Stephen Wolfram

(originally published in 1985 in Physica Scripta T9: 170–183)
Context: Problem 9. What is the correspondence between cellular automata and continuous systems?
Cellular automatat are discrete in several respects. First, they consist of a discrete spatial lattice of sites. Second, they evolve in discrete steps. And finally, each site has only a finite discrete set of possible values.
The first two forms of discreteness are addressed in the numerical analysis of approximate solutions to, say, differential equations....
The third form of discreteness in cellular automata is not so familiar from numerical analysis. It is an extreme form of round-off, in which each "number" can have only a few possible values (rather than the usual 216 or 232).

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Stephen Wolfram 16

British-American computer scientist, mathematician, physici… 1959

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