AI 中文总结
本研究综述哈希化学建模框架，扩展结构细胞哈希化学（SCHC）纳入空间局部性与二元竞争，用GPU加速在大空间域中揭示空间大小对其演化动力学的调控机制，展现其作为跨尺度开放演化研究测试平台的潜力。
AI 中文摘要
哈希化学是一类极简演化模型，其中确定性哈希函数为任意大小的实体分配标量分数，开辟了组合上极为庞大的可能性空间（即“基数跃迁”）。自提出以来，该思想已在多种场景中实现，从最初的空间形式到快速非空间变体，再到结构细胞模型。本文将哈希化学系列作为一个连贯的建模框架进行综述，并用它探究极简系统如何展现多尺度开放-ended演化动力学背后的机制。最新模型结构细胞哈希化学（SCHC）已成功以计算高效的方式展现了复制子的多尺度生态相互作用/适应及复杂度增长。本研究首先扩展SCHC，纳入复制结构间竞争相互作用的空间局部性与二元性，结果表明该扩展显著增强了SCHC的演化动力学；此外，我们使用GPU加速实现，在大得多的空间域中探究SCHC，发现空间大小作为控制参数，在紧凑复制子 regime 与失控规模主导 regime 之间引发类成核的随机转变，且我们将负责机制分为非空间的规模偏向采样反馈与有限尺寸空间效应。综上，这些结果展现了哈希化学作为极简、机制透明的测试平台，用于研究跨尺度开放-ended演化的巨大潜力。
英文摘要
Hash Chemistry is a family of minimalistic evolutionary models in which a deterministic hash function assigns a scalar score to entities of arbitrary size, opening a combinatorially vast possibility space (a ``cardinality leap''). Since its introduction, the idea has been realized in several settings, from the original spatial formulation to a fast non-spatial variant and then to structural cellular models. Here we review the Hash Chemistry family as a coherent modeling framework and use it to explore how minimal systems can demonstrate the mechanisms behind multiscale open-ended evolutionary dynamics. The most recent model, Structural Cellular Hash Chemistry (SCHC), successfully demonstrated multiscale ecological interaction/adaptation and complexity growth of replicators in a computationally efficient manner. In this study, we first extend SCHC to incorporate spatial locality and dyadicity of competitive interactions among replicating structures. We show this extension substantially enhances SCHC's evolutionary dynamics. Furthermore, we explore SCHC in a significantly larger spatial domain using a GPU-accelerated implementation. We show that the size of the space acts as a control parameter for a stochastic, nucleation-like transition between a compact-replicator regime and a runaway size-dominance regime, and we separate the responsible mechanism into a non-spatial, size-biased sampling feedback and a finite-size spatial effect. Altogether, these results illustrate the rich potential of Hash Chemistry as a minimal, mechanistically transparent testbed for studying open-ended evolution across scales.
Comments26 pages, 9 figures, 4 tables
