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

TL;DR

This work tackles the challenge of automatic discovery of diverse, lifelike patterns in Lenia by integrating Quality-Diversity (QD) methods. It introduces Leniabreeder, a framework that employs both MAP-Elites (manual diversity criteria) and AURORA (unsupervised diversity) to evolve a repertoire of autonomous solitons in Lenia, using a mix of handcrafted and latent-space descriptors and fitnesses. The study provides empirical evidence of sustained diversity and opens pathways toward in silico open-ended evolution, while acknowledging current limitations and outlining future improvements such as improved invariances in representation. Overall, the approach demonstrates that QD can unlock substantial artificial biodiversity within Lenia, offering a scalable route to exploring open-ended dynamics in complex artificial life systems.

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.

Figures (5)

• Figure 1: The world configuration $\mathbf{A}$ is cropped around the center of mass of the phenotype to form the $32 \times 32 \times 3$ input to the encoder (blue). Then, the encoder compresses the high-dimensional input into a low-dimensional latent vector $\mathbf{z}$ (green). During training, the decoder (red) transforms the latent vector back to the original input to compute a reconstruction loss, that is optimized via gradient descent.
• Figure 2: The phenotype at different timesteps forms a trajectory in the latent space $\mathcal{Z}$. The green dot represents the mean vector of the latent trajectory, i.e., the unsupervised descriptor of the individual. The red segments represent the Euclidean distance between the latent vectors and the descriptor, used to compute the unsupervised fitness of the individual.
• Figure 3: MAP-Elites Each row displays a single, independent run with each image sized $128 \times 128 \times 3$. Row 1 features individuals selected for velocity average fitness and color descriptor, arrayed from left to right to showcase proximity to specific colors such as red $[1, 0, 0]$, green $[0, 1, 0]$, blue $[0, 0, 1]$, red-green, red-blue, blue-green, red-green-blue and random $[0.01, 0.6, 0.5]$. Row 2 focuses on negative angle variance for fitness with mass and velocity as descriptors, showing a gradient of increasing mass and constant velocity. Row 3 highlights negative mass variance for fitness with angle and velocity as descriptors, arranging samples by different angles, clockwise rotation, counterclockwise rotation and no rotation.
• Figure 4: AURORA Each block of rows displays a single, independent run with each image sized $64 \times 64 \times 3$. Row 1-3 Fitness is the negative angle variance. Row 4-5 Fitness is the negative mass variance. Row 6-8 Fitness is unsupervised.
• Figure 5: AURORA 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.