AUTHOR=Verrelli Cristiano Maria , Iosa Marco , Roselli Paolo , Pisani Antonio , Giannini Franco , Saggio Giovanni 

TITLE=Generalized Finite-Length Fibonacci Sequences in Healthy and Pathological Human Walking: Comprehensively Assessing Recursivity, Asymmetry, Consistency, Self-Similarity, and Variability of Gaits

JOURNAL=Frontiers in Human Neuroscience

VOLUME=15

YEAR=2021

URL=https://www.frontiersin.org/journals/human-neuroscience/articles/10.3389/fnhum.2021.649533

DOI=10.3389/fnhum.2021.649533

ISSN=1662-5161

ABSTRACT=<p>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 <italic>composite gait cycle</italic>, 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 Φ<italic>-bonacci gait number</italic>, 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.</p>