Healthy and pathological human walking are here interpreted, from a temporal point of view, by means of dynamics-on-graph concepts and generalized finite-length Fibonacci sequences. Such sequences, in their most general definition, concern two sets of eight specific time intervals for the newly defined composite gait cycle, which involves two specific couples of overlapping (left and right) gait cycles. The role of the golden ratio, whose occurrence has been experimentally found in the recent literature, is accordingly characterized, without resorting to complex tools from linear algebra. Gait recursivity, self-similarity, and asymmetry (including double support sub-phase consistency) are comprehensively captured. A new gait index, named Phi-bonacci gait number, and a new related experimental conjecture - concerning the position of the foot relative to the tibia - are concurrently proposed. Experimental results on healthy or pathological gaits support the theoretical derivations.

中文翻译：

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健康和病态人类行走中的广义有限长度斐波那契数列：全面评估步态的递归性、不对称性、一致性、自相似性和可变性

从时间的角度来看，健康和病态的人类步行在这里是通过动态图概念和广义有限长度斐波那契数列来解释的。这些序列，在其最一般的定义中，涉及新定义的复合步态周期的两组八个特定时间间隔，其中涉及两个特定的重叠（左和右）步态周期对。黄金分割率的作用已在最近的文献中通过实验发现，因此具有特征性，无需求助于线性代数的复杂工具。步态递归性、自相似性和不对称性（包括双支撑子阶段一致性）被全面捕获。一个新的步态指数，名为 Phi-bonacci 步态数，同时提出了一个新的相关实验猜想——关于脚相对于胫骨的位置。健康或病理步态的实验结果支持理论推导。