The Collatz process embeds a base conversion algorithm

@inproceedings{Sterin2020TheCP,
  title={The Collatz process embeds a base conversion algorithm},
  author={Tristan St'erin and Damien Woods},
  booktitle={RP},
  year={2020}
}
The Collatz process is defined on natural numbers by iterating the map $T(x) = T_0(x) = x/2$ when $x\in\mathbb{N}$ is even and $T(x)=T_1(x) =(3x+1)/2$ when $x$ is odd. In an effort to understand its dynamics, and since Generalised Collatz Maps are known to simulate Turing Machines [Conway, 1972], it seems natural to ask what kinds of algorithmic behaviours it embeds. We define a quasi-cellular automaton that exactly simulates the Collatz process on the square grid: on input $x\in\mathbb{N… 

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