@inproceedings{Kari2012,
  author    = {{Kari, Jarkko}},
  title     = {{Cellular Automata, the Collatz Conjecture and Powers of 3/2}},
  booktitle = {{Developments in Language Theory}},
  publisher = {{Springer Berlin Heidelberg}},
  year      = {{2012}},
  pages     = {{40--49}},
  doi       = {{10.1007/978-3-642-31653-1_5}},
  url       = {{https://link.springer.com/chapter/10.1007/978-3-642-31653-1_5}},
  abstract  = {{We discuss one-dimensional reversible cellular automata F{\texttimes}3 and F{\texttimes}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,{łdots},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{\texttimes}3/2. We also remark that the automaton F{\texttimes}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.}},
  isbn      = {{978-3-642-31653-1}},
  address   = {{Berlin, Heidelberg}},
  editor    = {{Yen, Hsu-Chun
and Ibarra, Oscar H.}},
}