Using fractal analyses to study events allows us to capture the scale-independence of those events, that is, no matter at which level we study a phenomenon, we should get roughly the same results because events exhibit similar structure across scales. This is demonstrably true in mathematical fractals but is less assured in behavioral fractals. The current research directly tests the scale-independence hypothesis in the behavioral domain by exploring the fractal structure of aggression, a social phenomenon comprising events that span temporal scales from minutes of face-to-face arguments to centuries of international armed conflicts. Using publicly available data, we examined the temporal fractal structure of four scales of aggression: wars (very macrolevel, worldwide data), riots (macrolevel, worldwide data), violent crimes (microlevel, data gathered from cities and towns in the United States of America), and body movement during arguments (very microlevel, data gathered on American participants). Our results lend mixed support to the scale-independence hypothesis and provide insight into the self-organization of human interactions.

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与规模无关的侵略：人类侵略的四个层次的分形分析

使用分形分析来研究事件使我们能够捕获那些事件的尺度独立性，也就是说，无论我们在哪个级别研究现象，我们都应该得到大致相同的结果，因为事件在各个尺度上都表现出相似的结构。这在数学分形中可以证明是正确的，但在行为分形中却不能保证。当前的研究通过探索侵略的分形结构来直接检验行为领域的规模独立性假设，侵略的分形结构是一种社会事件，包括跨越时间尺度的事件，从面对面的辩论到数百年的国际武装冲突。利用公开可用的数据，我们研究了四种侵略尺度的时间分形结构：战争（非常宏观的，世界范围的数据），骚乱（宏观层面，全球数据），暴力犯罪（微观层面，从美国城镇获取的数据）以及论据期间的身体运动（微观层面，针对美国参与者的数据）。我们的结果为尺度独立性假设提供了混合支持，并为人类互动的自组织提供了见解。