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\iteman{io-port 06101625}
\itemau{Kari, Jarkko}
\itemti{Cellular automata, the Collatz conjecture and powers of 3/2.}
\itemso{Yen, Hsu-Chun (ed.) et al., Developments in language theory. 16th international conference, DLT 2012, Taipei, Taiwan, August 14-17, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-31652-4/pbk). Lecture Notes in Computer Science 7410, 40-49 (2012).}
\itemab
Summary: We discuss one-dimensional reversible cellular automata $F _{\times 3}$ and $F _{\times 3/2}$ that multiply numbers by 3 and 3/2, respectively, in base 6. They have the property that the orbits of all non-uniform 0-finite configurations contain as factors all finite words over the state alphabet $\{0,1,\cdots ,5\}$. Multiplication by 3/2 is conjectured to even have an orbit of 0-finite configurations that is dense in the usual product topology. An open problem by K. Mahler about $Z$-numbers has a natural interpretation in terms the automaton $F _{\times 3/2}$. We also remark that the automaton $F _{\times 3}$ that multiplies by 3 can be slightly modified to simulate the Collatz function. We state several open problems concerning pattern generation by cellular automata.
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\itemli{doi:10.1007/978-3-642-31653-1\_5}
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