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：本研究项目探究了莱尼亚（Lenia）这一模拟数字生物生态系统的虚拟生命平台。莱尼亚生态系统由简单的虚拟生物构成，这些生物能够运动、消耗、生长和繁殖。该平台作为研究虚拟生命与进化的工具具有重要意义，因其提供了可扩展且灵活的环境，可生成具有不同能力与行为的多样化生物体。衡量莱尼亚中的复杂性是本研究的关键，通过识别用于度量规则长期复杂涌现行为的指标，旨在进化出尚未发现的更优莱尼亚行为。遗传算法以邻域或核作为基因型，同时固定莱尼亚的其他参数（如生长函数），以生成对应于种群的多样化行为，并通过计算适应度值判定所产生行为的复杂性。首先，我们采用时间变异度作为适应度函数，对帧间方差较大的行为给予奖励。其次，我们采用基于自动编码器的适应度，奖励帧序列重建损失列表的变异度。第三，我们实施联合适应度，对重建帧像素密度的较高变异度进行奖励。所有三项实验均通过调整像素存活阈值与帧数进行优化。最后，在每项适应度分别执行9次500代实验后，从各实验中选取具有进一步进化潜力的配置，并运行至2500代。结果表明，核的质心随着特定像素集的增加而移动，并与边界共同促使核趋于高斯分布。