Many systems exhibit complex interactions between their components: some features or actions amplify each other's effects, others provide redundant information, and some contribute independently. We present a simple geometric method for discovering interactions and redundancies: when elements are added in random sequential orders and their contributions plotted over many trials, characteristic L-shaped patterns emerge that directly reflect interaction structure. The approach quantifies how the contribution of each element depends on those added before it, revealing patterns that distinguish interaction, independence, and redundancy on a unified scale. When pairwise contributions are visualized as two--dimensional point clouds, redundant pairs form L--shaped patterns where only the first-added element contributes, while synergistic pairs form L--shaped patterns where only elements contribute together. Independent elements show order--invariant distributions. We formalize this with the L--score, a continuous measure ranging from $-1$ (perfect synergy, e.g. $Y=X_1X_2$) to $0$ (independence) to $+1$ (perfect redundancy, $X_1 \approx X_2$). The relative scaling of the L--shaped arms reveals feature dominance in which element consistently provides more information. Although computed only from pairwise measurements, higher--order interactions among three or more elements emerge naturally through consistent cross--pair relationships (e.g. AB, AC, BC). The method is metric--agnostic and broadly applicable to any domain where performance can be evaluated incrementally over non-repeating element sequences, providing a unified geometric approach to uncovering interaction structure.

翻译：许多系统在其组件间展现出复杂的交互作用：某些特征或行为会相互放大彼此的影响，另一些则提供冗余信息，还有一些独立发挥作用。我们提出一种发现交互与冗余的简单几何方法：当元素以随机顺序依次添加，并在多次试验中绘制其贡献度时，会出现特征性的L形模式，直接反映交互结构。该方法量化每个元素的贡献如何依赖于先前添加的元素，从而在统一尺度上揭示区分交互、独立性和冗余的模式。当成对贡献以二维点云可视化时，冗余对形成L形模式——仅先添加的元素产生贡献，而协同对形成L形模式——仅当元素共同作用时才产生贡献。独立元素则呈现顺序不变的分布。我们通过L分数对此进行形式化定义：这是一个连续度量，范围从$-1$（完全协同，例如$Y=X_1X_2$）到$0$（独立）再到$+1$（完全冗余，$X_1 \approx X_2$）。L形臂的相对比例揭示了特征主导性，即哪个元素始终提供更多信息。尽管仅通过成对测量计算，但三个及以上元素间的高阶交互可通过一致的跨对关系（例如AB、AC、BC）自然涌现。该方法与具体度量无关，可广泛应用于任何能够通过非重复元素序列进行增量性能评估的领域，为揭示交互结构提供了一种统一的几何分析框架。