Cellular automata (CA), originally developed as computational models of natural processes, have become a central subject in the study of complex systems and generative visual forms. Among them, the Ulam-Warburton Cellular Automaton (UWCA) exhibits recursive growth and fractal-like characteristics in its spatial evolution. However, exact self-similar fractal structures are typically observable only at specific generations and remain visually obscured in conventional binary renderings. This study introduces a Recursive Gradient Profile Function (RGPF) that assigns grayscale values to newly activated cells according to their generation index, enabling latent self-similar structures to emerge cumulatively in spatial visualizations. Through this gradient-based mapping, recursive geometric patterns become perceptible across scales, revealing fractal properties that are not apparent in standard representations. We further extend this approach to UWCA variants with alternative neighborhood configurations, demonstrating that these rules also produce distinct yet consistently fractal visual patterns when visualized using recursive gradient profile. Beyond computational analysis, the resulting generative forms resonate with optical and cultural phenomena such as infinity mirrors, video feedback, and mise en abyme in European art history, as well as fractal motifs found in religious architecture. These visual correspondences suggest a broader connection between complexity science, computational visualization, and cultural art and design.

翻译：元胞自动机（CA）最初作为自然过程的计算模型被提出，现已成为复杂系统和生成视觉形态研究的核心课题。其中，乌拉姆-沃伯顿元胞自动机（UWCA）在其空间演化中展现出递归生长和类分形特征。然而，精确的自相似分形结构通常仅在特定世代可见，且在传统的二值化渲染中仍存在视觉遮蔽。本研究提出一种递归梯度剖面函数（RGPF），该函数根据新激活细胞的世代索引为其分配灰度值，使得潜在的自相似结构能够在空间可视化中累积显现。通过这种基于梯度的映射，递归几何模式在不同尺度上变得可感知，从而揭示了标准表示中不明显的分形特性。我们进一步将这种方法扩展到具有替代邻域配置的UWCA变体，证明这些规则在使用递归梯度剖面可视化时，同样会产生独特且具有一致分形特征的视觉模式。除计算分析外，所生成的形态与光学及文化现象产生共鸣，例如无限镜、视频反馈、欧洲艺术史中的嵌套结构（mise en abyme），以及宗教建筑中出现的分形图案。这些视觉关联表明，在复杂性科学、计算可视化和文化艺术设计之间存在着更广泛的联系。