The design of complex self-organising systems producing life-like phenomena,
such as the open-ended evolution of virtual creatures, is one of the main goals
of artificial life. Lenia, a family of cellular automata (CA) generalizing
Conway's Game of Life to continuous space, time and states, has attracted a lot
of attention because of the wide diversity of self-organizing patterns it can
generate. Among those, some spatially localized patterns (SLPs) resemble
life-like artificial creatures and display complex behaviors. However, those
creatures are found in only a small subspace of the Lenia parameter space and
are not trivial to discover, necessitating advanced search algorithms.
Furthermore, each of these creatures exist only in worlds governed by specific
update rules and thus cannot interact in the same one. This paper proposes as
mass-conservative extension of Lenia, called Flow Lenia, that solve both of
these issues. We present experiments demonstrating its effectiveness in
generating SLPs with complex behaviors and show that the update rule parameters
can be optimized to generate SLPs showing behaviors of interest. Finally, we
show that Flow Lenia enables the integration of the parameters of the CA update
rules within the CA dynamics, making them dynamic and localized, allowing for
multi-species simulations, with locally coherent update rules that define
properties of the emerging creatures, and that can be mixed with neighbouring
rules. We argue that this paves the way for the intrinsic evolution of
self-organized artificial life forms within continuous CAs.

本文提出了一种名为 Flow Lenia 的细胞自动机扩展，解决了 Lenia 中存在的一些问题，包括虚拟生物只存在于特定规则的世界中且规则不可交互，证明了 Flow Lenia 在生成具有复杂行为的空间局部模式方面的有效性，并展示了它在动态和本地化的 CA 动力学中的潜力，扩展了 CA 模拟的应用范围，为自组织人工生命的内在进化铺平了道路。

Flow-Lenia: 基于质量守恒和参数本地化的元胞自动机开放式演化

Flow-Lenia: Towards open-ended evolution in cellular automata through mass conservation and parameter localization

Reproduction, development, and individual interactions are essential topics
in artificial life. The cellular automata, which can handle these in a
composite way, is highly restricted in its form and behavior because it
represents life as a pattern of cells. In contrast, the virtual creatures
proposed by Karl Sims have a very high degree of freedom in terms of morphology
and behavior. However, they have limited expressive capacity in terms of those
viewpoints. This study carefully extracts the characteristics of the cellular
automata and Sims models to propose a new artificial life model that can
simulate reproduction, development, and individual interactions while
exhibiting high expressive power for morphology and behavior. The simulation
was performed by sequentially reading a book with genetic information and
repeatedly executing four actions: expansion, connection, disconnection, and
transition. The virtual creatures in the proposed model exhibit unique survival
strategies and lifestyles and acquire interesting properties in reproduction,
development, and individual interactions while having freedom in morphology and
behavior.

本文介绍了一种新的人工生命模型，可以模拟细胞自动机和虚拟生物的特征，实现了形态和行为上高度自由的同时又能模拟繁殖、发展、个体互动等生命特征。通过阅读遗传信息的方式，执行扩张、连接、断开和过渡四个动作，模拟出了具有独特的生存策略和生活方式，同时在繁殖、发展和个体互动方面获得了有趣的性质。