The paleoenvironment influences trace-making behavior significantly, and progressively more evidence shows that this behavior follows scale-invariance properties. In this study, we focused on the definition of behavioral complexity in the trace fossil Zoophycos to explore its paleoenvironmental significance. Firstly, the fractal topography in Zoophycos was established by introducing virtual tertiary lamellae. Next, a fractal dimension (D) model was proposed and the spatio-temporal evolution trend of the complexity of the trace-making behavior was established. In application, the correlation of D to the paleo-water depth and substrate consistency of the paleoenvironment was analyzed with the aid of variations of δ13C and lamellae deformations in Zoophycos from the Carboniferous-Permian Taiyuan Formation of North China. The results show that D increases with paleo-water depth, although it decreases when the degree of substrate consistency increases. Our investigation indicates that fractal topography not only provides an essential explanation for the complexity of trace-making behavior but also plays a reliable and significant role in paleoenvironmental interpretation. Most importantly, this work may shed some light on the subject of fractal ichnology and provide a mathematical framework toward studies in quantitative ichnology.

中文翻译：

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海洋痕迹化石中行为复杂性的特征及其古环境意义：动物藻类的案例研究

古环境显着影响示踪行为，越来越多的证据表明这种行为遵循尺度不变性。在这项研究中，我们重点研究了痕迹化石中行为复杂性的定义。动物藻类探索其古环境意义。首先，分形地形动物藻类是通过引入虚拟第三层薄片而建立的。接下来，分形维数（D)模型，建立了寻迹行为复杂度的时空演化趋势。在应用中，相关性D分析了古环境的古水深和基质一致性δ13C 和薄片变形动物藻类来自华北石炭-二叠统太原组。结果表明D随古水深而增加，但随着底物稠度的增加而减少。我们的调查表明，分形地形不仅为示踪行为的复杂性提供了必要的解释，而且在古环境解释中也发挥着可靠和重要的作用。最重要的是，这项工作可能会为分形技术主题提供一些启示，并为定量技术研究提供一个数学框架。