# Computational Hierarchy of Elementary Cellular Automata

arXiv: https://arxiv.org/abs/2108.00415 · HTML: https://mlsanity.com/paper/2108.00415/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 30 references that are in the map.
- First posted on arXiv 1 Aug 2021.

## Builds on (most cited first, 1 of 1)

- [Classification of Complex Systems Based on Transients](https://mlsanity.com/paper/2008.13503/) (2020)

## Built on by (most cited first, 2 of 2)

- [On when is Reservoir Computing with Cellular Automata Beneficial?](https://mlsanity.com/paper/2407.09501/) (2024)
- [A Sensitivity Analysis of Cellular Automata and Heterogeneous Topology Networks: Partially-Local Cellular Automata and Homogeneous Homogeneous Random Boolean Networks](https://mlsanity.com/paper/2407.18017/) (2024)

## Abstract (arXiv)

The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the ability of automata to emulate one another, and we use this notion to define such a set of naturally emerging tasks. We present the results for elementary cellular automata, although the core ideas can be extended to other computational systems. We compute a graph showing which elementary cellular automata can be emulated by which and show that certain chaotic automata are the only ones that cannot emulate any automata non-trivially. Finally, we use the emulation notion to suggest a novel definition of chaos that we believe is suitable for discrete computational systems. We believe our work can help design parallel computational systems that are Turing-complete and also computationally efficient.