Multifractal Auditory Stimulation Promotes the Effect of Multifractal Torso Sway on Spatial Perception: Evidence from Distance Perception by Blindwalking

Stimulation and movement interact non-linearly across multiple scales—a point empirically and quantitatively available through multifractal structure. Multifractal movements might implicate multifractal stimulation. Previous correlational modeling of accelerometry-measured torso movements during blindwalking indicated that multifractality in movement predicts distance-perceptual judgments. We now experimentally tested whether multifractal stimulation interacted with multifractal torso movement to support distance perception. We edited music-like sounds to manipulate multifractal non-linearity in auditory stimulation through headphones to participants perceiving distance by blindwalking—with eyes closed both during Lap-1 distance instruction and Lap-2 distance replication. Stimulation non-linearity significantly interacted with torso movements to predict distance-replication judgments. Low stimulation non-linearity showed no effect. Medium stimulation non-linearity interacted with Lap-2 torso non-linearity to produce over-/underestimation of shorter/longer distances. Higher auditory non-linearity led Lap-2 distance replication enlisted longer time scales, drawing on prior torso non-linearity, i.e. from Lap 1, and producing overestimation proportionally with a greater standard deviation of torso movements. Distance perception by blindwalking appears more accurate under medium rather than excessive non-linearity, resonating with previous evidence that walking engenders less multifractality than other movements. Movement-dependence of stimulation is also unsurprising to ecological-psychology wisdom. However, to our knowledge, present results constitute an unprecedented step toward elaborating movement-dependence to multifractal-geometrical approaches to perception.

刺激与运动在多尺度下呈现非线性交互——该特性可通过多重分形（multifractal）结构从实证与定量维度得以验证。多重分形运动可能关联多重分形刺激。此前针对盲走任务（blindwalking）中经加速度测量法（accelerometry）获取的躯干运动开展的相关建模研究显示，运动中的多重分形特性可预测距离知觉判断结果。
本研究通过实验验证了多重分形刺激与多重分形躯干运动是否会交互作用以支持距离知觉。我们通过耳机向被试呈现经编辑的类音乐声音，以此操控听觉刺激中的多重分形非线性特性；被试需在闭眼状态下完成第一圈（Lap-1）的距离学习与第二圈（Lap-2）的距离复刻任务。
结果表明，刺激非线性程度与躯干运动存在显著交互作用，可共同预测距离复刻判断结果。低水平的刺激非线性未呈现显著效应；中等水平的刺激非线性则与第二圈躯干运动的非线性特征相互作用，引发对短距离的高估与长距离的低估。更高水平的听觉非线性则会使第二圈距离复刻任务调用更长的时间尺度，并依托第一圈的躯干运动非线性特征，随躯干运动标准差的增加成比例地产生高估效应。
盲走任务下的距离知觉在中等而非过度的非线性条件下更为准确，这与既往研究结论相符——步行运动的多重分形程度低于其他运动类型。刺激的运动依赖性也符合生态心理学（ecological psychology）的经典观点。但据我们所知，本研究结果首次将运动依赖性拓展至知觉的多重分形几何研究范式（multifractal-geometrical approaches）框架中，是该领域前所未有的重要进展。