Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans' ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D. In Experiment 2, participants completed a map-reading and location-judgment task in separate sets of fractal landscapes. In both experiments, task performance was highest at the low-to-mid range of D, which was previously reported as most preferred and discriminable in studies of fractal aesthetics and discrimination, respectively, supporting a theory of visual fluency. The applicability of these findings to architecture, urban planning, and the general design of constructed spaces is discussed.

中文翻译：

---

虚拟环境中的导航性能随景观的分形维数而变化

分形几何已被用于描述自然和建筑环境，但尚未在导航研究中进行研究。为了建立自然环境的分形维数 (D) 与人类在此类空间中导航的能力之间的关系，我们使用模拟自然分形特性的虚拟环境进行了两项实验。在实验 1 中，参与者在有或没有地图的 D 中变化的景观中完成了目标驱动的搜索任务。在实验 2 中，参与者在不同的分形景观集中完成了地图阅读和位置判断任务。在这两个实验中，任务表现在 D 的中低范围内最高，这在以前分别被报道为分形美学和辨别研究中最优选和最可区分的，支持视觉流畅性理论。讨论了这些发现对建筑、城市规划和建筑空间总体设计的适用性。