# Looking for Complexity at Phase Boundaries in Continuous Cellular Automata

arXiv: https://arxiv.org/abs/2402.17848 · HTML: https://mlsanity.com/paper/2402.17848/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2024.

## Built on by (most cited first, 3 of 3)

- [Expedition & Expansion: Leveraging Semantic Representations for Goal-Directed Exploration in Continuous Cellular Automata](https://mlsanity.com/paper/2509.03863/) (2025)
- [Visualizing the Structure of Lenia Parameter Space](https://mlsanity.com/paper/2601.01932/) (2026)
- [Complex System Exploration with Interactive Human Guidance](https://mlsanity.com/paper/2510.00794/) (2025)

## Abstract (arXiv)

One key challenge in Artificial Life is designing systems that display an emergence of complex behaviors. Many such systems depend on a high-dimensional parameter space, only a small subset of which displays interesting dynamics. Focusing on the case of continuous systems, we introduce the 'Phase Transition Finder'(PTF) algorithm, which can be used to efficiently generate parameters lying at the border between two phases. We argue that such points are more likely to display complex behaviors, and confirm this by applying PTF to Lenia showing it can increase the frequency of interesting behaviors more than two-fold, while remaining efficient enough for large-scale searches.