# Intrinsically Motivated Discovery of Diverse Patterns in Self-Organizing Systems

arXiv: https://arxiv.org/abs/1908.06663 · HTML: https://mlsanity.com/paper/1908.06663/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2019.

## Built on by (most cited first, 13 of 13)

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- [Arbitrarily Scalable Environment Generators via Neural Cellular Automata](https://mlsanity.com/paper/2310.18622/) (2023)
- [Discovering Sensorimotor Agency in Cellular Automata using Diversity Search](https://mlsanity.com/paper/2402.10236/) (2024)
- [Generalization over different cellular automata rules learned by a deep feed-forward neural network](https://mlsanity.com/paper/2103.14886/) (2021)
- [ACES: Generating Diverse Programming Puzzles with with Autotelic Generative Models](https://mlsanity.com/paper/2310.10692/) (2023)
- [A Path to Universal Neural Cellular Automata](https://mlsanity.com/paper/2505.13058/) (2025)
- [Habits and goals in synergy: a variational Bayesian framework for behavior](https://mlsanity.com/paper/2304.05008/) (2023)
- [Exploring Flow-Lenia Universes with a Curiosity-driven AI Scientist: Discovering Diverse Ecosystem Dynamics](https://mlsanity.com/paper/2505.15998/) (2025)
- [Expedition & Expansion: Leveraging Semantic Representations for Goal-Directed Exploration in Continuous Cellular Automata](https://mlsanity.com/paper/2509.03863/) (2025)
- [Equilibrium flow: From Snapshots to Dynamics](https://mlsanity.com/paper/2509.17990/) (2025)
- [Complex System Exploration with Interactive Human Guidance](https://mlsanity.com/paper/2510.00794/) (2025)

## Abstract (arXiv)

In many complex dynamical systems, artificial or natural, one can observe self-organization of patterns emerging from local rules. Cellular automata, like the Game of Life (GOL), have been widely used as abstract models enabling the study of various aspects of self-organization and morphogenesis, such as the emergence of spatially localized patterns. However, findings of self-organized patterns in such models have so far relied on manual tuning of parameters and initial states, and on the human eye to identify interesting patterns. In this paper, we formulate the problem of automated discovery of diverse self-organized patterns in such high-dimensional complex dynamical systems, as well as a framework for experimentation and evaluation. Using a continuous GOL as a testbed, we show that recent intrinsically-motivated machine learning algorithms (POP-IMGEPs), initially developed for learning of inverse models in robotics, can be transposed and used in this novel application area. These algorithms combine intrinsically-motivated goal exploration and unsupervised learning of goal space representations. Goal space representations describe the interesting features of patterns for which diverse variations should be discovered. In particular, we compare various approaches to define and learn goal space representations from the perspective of discovering diverse spatially localized patterns. Moreover, we introduce an extension of a state-of-the-art POP-IMGEP algorithm which incrementally learns a goal representation using a deep auto-encoder, and the use of CPPN primitives for generating initialization parameters. We show that it is more efficient than several baselines and equally efficient as a system pre-trained on a hand-made database of patterns identified by human experts.