# Universal One-Dimensional Cellular Automata Derived for Turing Machines and its Dynamical Behaviour

## TL;DR

This paper introduces an algorithm to convert any Turing machine into a one-dimensional cellular automaton, demonstrating universality and analyzing its dynamical behavior through specific examples.

## Contribution

It presents a novel algorithm for converting Turing machines into one-dimensional cellular automata with linear time complexity, including examples of universal automata.

## Key findings

- Successfully converted binary sum, rule 110, and a universal reversible Turing machine into cellular automata.
- Demonstrated the universality and dynamical behavior of the resulting automata.
- Provided insights into the spatial dynamics of these automata.

## Abstract

Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular automaton with a 2-linear time and display its spatial dynamics. Three particular Turing machines are converted in three universal one-dimensional cellular automata, they are: binary sum, rule 110 and a universal reversible Turing machine.