A Quantitative Study of Film Color in The Grand Budapest Hotel Based on Birkhoff's Theory

基于伯克霍夫理论对电影《布达佩斯大饭店》的色彩量化研究

Wes Anderson's film The Grand Budapest Hotel is world-renowned for its highly stylized and harmoniously unified visual aesthetics. In the film, color serves not only as a narrative element but also as a core carrier for constructing the emotional tone and thematic connotations. However, existing studies mostly focus on qualitative descriptions and stylistic summaries of its color application, lacking objective quantitative data support, which makes it difficult to accurately interpret the scientific mechanism behind the generation of its aesthetic effects. To address this gap, this study employs George David Birkhoff's aesthetic measure model formula (M = O/C), quantifying aesthetic perception as the ratio of order (O) to complexity (C). By analyzing the color contrast relationships in the film's color compositions and the correspondence between colors and narrative structures, an evaluation system for its “degree of order” (O) is constructed, enabling a quantitative and interdisciplinary exploration of the film's color aesthetics. This research successfully extends Birkhoff's model—originally applied to the aesthetic measurement of static geometric figures—to film color analysis. It not only provides an objective and innovative perspective for interpreting the visual charm of The Grand Budapest Hotel but also verifies the applicability and effectiveness of the model in image art research. Furthermore, it offers a referable quantitative research methodology for film aesthetics studies and color design practices in digital media art.

韦斯·安德森执导的电影《布达佩斯大饭店》以其高度风格化且和谐统一的视觉美学而享誉世界。在影片中，色彩不仅作为叙事要素存在，同时也是构建情绪基调与主题内涵的核心载体。然而，现有研究多集中于对其色彩运用的定性描述与风格性总结，缺乏客观的量化数据支持，这在一定程度上限制了对其美学效果生成之科学机制的准确阐释。为弥补这一不足，本文引入乔治·大卫·伯克霍夫的美学度量模型公式（M = O / C），将审美感知量化为秩序度（O）与复杂度（C）的比值。通过分析影片色彩构成中的色彩对比关系以及色彩与叙事结构之间的对应关系，构建其“秩序度”（O）的评价体系，从而对影片色彩美学展开定量化与跨学科的研究。研究将原本用于静态几何图形美学测量的伯克霍夫模型成功拓展至电影色彩分析领域，不仅为解读《布达佩斯大饭店》的视觉魅力提供了客观而创新的视角，也验证了该模型在图像艺术研究中的适用性与有效性。同时，本文为电影美学研究及数字媒体艺术中的色彩设计实践提供了一种可供借鉴的量化研究方法。