Browser fingerprinting has become a prevalent technique for tracking and identifying users online, posing significant privacy risks. The increasing variability in web browser configurations, coupled with the continuous evolution of browser features, presents complex challenges in understanding and mitigating the impact of fingerprinting. In this paper, we introduce a novel approach that combines feature modeling techniques with tree-based representations to capture the intricate relationships and constraints within browser fingerprints. By translating 22, 773 fingerprints into a feature model with 34, 557 nodes, we enable a comprehensive analysis of their variability and uniqueness across 1, 519 switches and 596 flags on 7 headless and headful browser versions. Our methodology facilitates various use cases, such as generating representative fingerprints for testing, detecting anomalies, and identifying discriminating attributes. We aim to provide developers and researchers with a powerful tool for studying browser fingerprints and developing effective strategies to enhance user privacy in the face of evolving tracking techniques.