# Evolving Structures in Complex Systems

arXiv: https://arxiv.org/abs/1911.01086 · HTML: https://mlsanity.com/paper/1911.01086/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2019.

## Built on by (most cited first, 6 of 6)

- [Illuminating Diverse Neural Cellular Automata for Level Generation](https://mlsanity.com/paper/2109.05489/) (2021)
- [Visualizing computation in large-scale cellular automata](https://mlsanity.com/paper/2104.01008/) (2021)
- [Exploring Flow-Lenia Universes with a Curiosity-driven AI Scientist: Discovering Diverse Ecosystem Dynamics](https://mlsanity.com/paper/2505.15998/) (2025)
- [Classification of Discrete Dynamical Systems Based on Transients](https://mlsanity.com/paper/2108.01573/) (2021)
- [Benchmarking Learning Efficiency in Deep Reservoir Computing](https://mlsanity.com/paper/2210.02549/) (2022)
- [Capturing Emerging Complexity in Lenia](https://mlsanity.com/paper/2305.09378/) (2023)

## Abstract (arXiv)

In this paper we propose an approach for measuring growth of complexity of emerging patterns in complex systems such as cellular automata. We discuss several ways how a metric for measuring the complexity growth can be defined. This includes approaches based on compression algorithms and artificial neural networks. We believe such a metric can be useful for designing systems that could exhibit open-ended evolution, which itself might be a prerequisite for development of general artificial intelligence. We conduct experiments on 1D and 2D grid worlds and demonstrate that using the proposed metric we can automatically construct computational models with emerging properties similar to those found in the Conway's Game of Life, as well as many other emergent phenomena. Interestingly, some of the patterns we observe resemble forms of artificial life. Our metric of structural complexity growth can be applied to a wide range of complex systems, as it is not limited to cellular automata.