  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.
