This research project investigates Lenia, an artificial life platform that simulates ecosystems of digital creatures. Lenia's ecosystem consists of simple, artificial organisms that can move, consume, grow, and reproduce. The platform is important as a tool for studying artificial life and evolution, as it provides a scalable and flexible environment for creating a diverse range of organisms with varying abilities and behaviors. Measuring complexity in Lenia is a key aspect of the study, which identifies the metrics for measuring long-term complex emerging behavior of rules, with the aim of evolving better Lenia behaviors which are yet not discovered. The Genetic Algorithm uses neighborhoods or kernels as genotype while keeping the rest of the parameters of Lenia as fixed, for example growth function, to produce different behaviors respective to the population and then measures fitness value to decide the complexity of the resulting behavior. First, we use Variation over Time as a fitness function where higher variance between the frames are rewarded. Second, we use Auto-encoder based fitness where variation of the list of reconstruction loss for the frames is rewarded. Third, we perform combined fitness where higher variation of the pixel density of reconstructed frames is rewarded. All three experiments are tweaked with pixel alive threshold and frames used. Finally, after performing nine experiments of each fitness for 500 generations, we pick configurations from all experiments such that there is a scope of further evolution, and run it for 2500 generations. Results show that the kernel's center of mass increases with a specific set of pixels and together with borders the kernel try to achieve a Gaussian distribution.

翻译：本研究项目探讨了Lenia这一模拟数字生物生态系统的人工生命平台。Lenia的生态系统由简单的、能够移动、消耗、生长和繁殖的人工生物构成。该平台作为研究人工生命和进化的工具具有重要意义，因为它提供了可扩展且灵活的环境，能够创造具有不同能力和行为的多样化生物体。衡量Lenia中的复杂性是本研究的一个关键方面，我们识别了用于衡量规则长期复杂新兴行为的指标，旨在进化出尚未发现的更优Lenia行为。遗传算法将邻域或核作为基因型，同时固定Lenia的其他参数（例如生长函数），以产生与种群相对应的不同行为，并通过测量适应度值来确定所得行为的复杂性。首先，我们使用随时间变化作为适应度函数，奖励帧间较高的方差。其次，我们采用基于自编码器的适应度，奖励帧重建损失列表的方差。第三，我们执行组合适应度，奖励重建帧像素密度的更高方差。所有三个实验都通过像素存活阈值和使用的帧数进行调整。最后，在对每个适应度进行九组实验（每组500代）后，我们从所有实验中选择具有进一步进化潜力的配置，并运行2500代。结果表明，核的质心随特定像素集而增加，并且核与边界一起趋向于实现高斯分布。