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.
View on arXiv@article{mouchoux2025_2503.17219,
title={ Cyber Campaign Fractals -- Geometric Analysis of Hierarchical Cyber Attack Taxonomies },
author={ Ronan Mouchoux and François Moerman },
journal={arXiv preprint arXiv:2503.17219},
year={ 2025 }
}