This paper introduces a novel mathematical framework for analyzing cyber threat campaigns through fractal geometry. By conceptualizing hierarchical taxonomies (MITRE ATT&CK, DISARM) as snowflake-like structures with tactics, techniques, and sub-techniques forming concentric layers, we establish a rigorous method for campaign comparison using Hutchinson's Theorem and Hausdorff distance metrics. Evaluation results confirm that our fractal representation preserves hierarchical integrity while providing a dimensionality-based complexity assessment that correlates with campaign complexity. The proposed methodology bridges taxonomy-driven cyber threat analysis and computational geometry, providing analysts with both mathematical rigor and interpretable visualizations for addressing the growing complexity of adversarial operations across multiple threat domains.

翻译：本文提出了一种基于分形几何分析网络威胁活动的新型数学框架。通过将层次化分类法（MITRE ATT&CK、DISARM）概念化为雪花状结构——其中策略、技术和子技术构成同心层，我们利用哈钦森定理和豪斯多夫距离度量建立了严格的活动比较方法。评估结果证实，我们的分形表示法在保持层次结构完整性的同时，提供了基于维度的复杂度评估，该评估与攻击活动复杂度具有相关性。所提出的方法论连接了分类法驱动的网络威胁分析与计算几何，为分析人员提供了兼具数学严谨性和可解释可视化的工具，以应对跨多威胁领域的对抗性操作日益增长的复杂性。