Toward Artificial Open-Ended Evolution within Lenia using Quality-Diversity

Maxence Faldor, Antoine Cully
Imperial College London
ALIFE 2024
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Leniabreeder automatically evolves a diverse population of self-organizing autonomous patterns.

Abstract

From the formation of snowflakes to the evolution of diverse life forms, emergence is ubiquitous in our universe. In the quest to understand how complexity can arise from simple rules, abstract computational models, such as cellular automata, have been developed to study self-organization. However, the discovery of self-organizing patterns in artificial systems is challenging and has largely relied on manual or semi-automatic search in the past.

In this paper, we show that Quality-Diversity, a family of Evolutionary Algorithms, is an effective framework for the automatic discovery of diverse self-organizing patterns in complex systems. Quality-Diversity algorithms aim to evolve a large population of diverse individuals, each adapted to its ecological niche. Combined with Lenia, a family of continuous cellular automata, we demonstrate that our method is able to evolve a diverse population of lifelike self-organizing autonomous patterns. Our framework, called Leniabreeder, can leverage both manually defined diversity criteria to guide the search toward interesting areas, as well as unsupervised measures of diversity to broaden the scope of discoverable patterns.

We demonstrate both qualitatively and quantitatively that Leniabreeder offers a powerful solution for discovering self-organizing patterns. The effectiveness of unsupervised Quality-Diversity methods combined with the rich landscape of Lenia exhibits a sustained generation of diversity and complexity characteristic of biological evolution. We provide empirical evidence that suggests unbounded diversity and argue that Leniabreeder is a step toward replicating open-ended evolution in silico.

Dive into Lenia ✨

Explore a population of Lenia solitons evolved with Quality-Diversity using unsupervised fitness and descriptor functions. Each soliton is displayed at its corresponding descriptor in descriptor space. The descriptor space is 6-dimensional and projected with t-SNE in a 3-dimensional space for visualization.

Method

We introduce Leniabreeder, a framework designed to automate the discovery of diverse autonomous patterns in complex systems. We formalize the discovery of diverse artificial species as an evolutionary algorithm, specifically a Quality-Diversity optimization problem.


We employ two approaches: MAP-Elites, using manually defined diversity criteria to steer the search toward areas of interest, and AURORA, using unsupervised descriptor and fitness functions circumventing the need for predefined diversity criteria and broadening the range of possible discoveries. Both methods follow a traditional QD loop of selection, variation, evaluation and addition.


AURORA is an unsupervised Quality-Diversity algorithm that automatically learns a diversity measure that defines the ecological niches of the population, not only influencing local competition within the current population but also shaping subsequent offspring evaluation and addition. This dynamic interaction between the individuals and their niches propels a cycle of discovery, where each individual adapts to its niche but also drives the realignment of niche boundaries.


Leniabreeder fosters artificial open-ended evolution.

The ongoing increase in population entropy and variance, coupled with the continuous introduction of new elites, highlights Leniabreeder's potential to drive open-ended evolution, aligning with some of the key dynamics — namely, the perpetual production of novelty, unbounded diversity, and continuous change in information content.

Entropy, variance and cumulative elites with different fitness functions. The solid line is the median and the shaded area represents the first and third quartiles.

Experiments

Click on a card to explore the experiment 🔎

MAP-Elites

Positive
Velocity
Average
Positive
Mass
Average
Positive
Mass
Variance
Negative
Angle
Variance
Negative
Mass
Variance

AURORA

Unsupervised
Positive
Velocity
Average
Negative
Mass
Average
Negative
Angle
Variance
Negative
Mass
Variance

Conclusion

We show that Quality-Diversity is an effective framework for the automatic discovery of diverse self-organizing patterns in complex systems. Our findings not only showcase the breadth of artificial life within Lenia but also underscore the relevance of Quality-Diversity algorithms in illuminating an ecosystem of artificial species and exhibiting a sustained generation of diversity. Combined with Lenia, we show that Quality-Diversity has the potential to present some hallmarks of open-ended evolution, aligning with its original purpose.

At the core of Leniabreeder lies the utilization of a novel unsupervised fitness function. Yet, it relies on simple heuristics that only mimics homeostasis. We posit that enhancing this fitness function would enable to discover even more meaningful expressions of artificial life. Furthermore, the current autoencoder architecture is not invariant to rotation or scaling. We believe that improving the autoencoder architecture could also benefit the framework to capture a more refined notion of diversity.

Related Links

There are several excellent works exploring the discovery of diverse patterns within Lenia. The paper "Intrinsically Motivated Discovery of Diverse Patterns in Self-Organizing Systems" uses IMGEP-based methods to uncover a range of patterns within Lenia. Another notable work, "Hierarchically-Organized Latent Modules for Exploratory Search in Morphogenetic Systems", employs IMGEP-HOLMES, where a hierarchy of embedding networks is actively constructed by the exploring agent to represent different niches of patterns discovered during the exploration loop.

Other works focus on open-endedness within Lenia. The paper "Towards Large-Scale Simulations of Open-Ended Evolution in Continuous Cellular Automata" suggests several factors that may facilitate open-ended evolution, such as virtual environment design, mass conservation, and energy constraints. Additionally, the study "Towards Open-Ended Evolution in Cellular Automata through Mass Conservation and Parameter Localization" proposes a mass-conservative extension of Lenia, called Flow Lenia, which encourages the design of microcosms where open-ended evolutionary processes can emerge through interspecies interactions.

BibTeX

@article{faldor2024leniabreeder,
	author    = {Faldor, Maxence and Cully, Antoine},
	title     = {Toward Artificial Open-Ended Evolution within Lenia using Quality-Diversity},
	journal   = {Artificial Life},
	year      = {2024},
}