# 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…

## 3 Citations

### Binary Expression of Ancestors in the Collatz Graph

- Mathematics, Computer ScienceRP
- 2020

This paper implements the algorithm which generates the regular expression, $\texttt{reg}_k(x)$ for any $x$ and $k, and gives a new exploratory tool for further study of the Collatz graph in binary.

### Small tile sets that compute while solving mazes

- Computer ScienceDNA
- 2021

Two tiny tile sets are given that are computationally universal in the Maze-Walking Tile Assembly Model and give two different methods to find simple universal tile sets, and provide motivation for using pre-assembled maze structures as circuit wiring diagrams in molecular self-assembly based computing.

### On the hardness of knowing busy beaver values BB(15) and BB(5, 4)

- MathematicsArXiv
- 2021

This paper puts a finite, albeit large, bound on Erdős’ conjecture, by making it equivalent to the following finite statement: for all 8 < n ≤ min(BB(15),BB(5, 4)) there is at least one digit 2 in the base 3 representation of 2.

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