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Hidden time-patterns in cyclic human movements: a matter of temporal Fibonacci sequence generation and harmonization
Cristiano Maria Verrelli1, Lucio Caprioli2, Marco Iosa3,4
1Department of Electronic Engineering, University of Rome Tor Vergata, Rome, Italy.
Frontiers in Human Neuroscience
|April 23, 2025
Summary
Generalized Fibonacci sequences reveal hidden self-similar patterns in human movements like walking and tennis. This mathematical understanding aids in analyzing and potentially automating complex gestures.
Area of Science:
- Biomechanics and Movement Analysis
- Mathematical Modeling of Human Motion
- Cognitive Science and Motor Learning
Background:
- Fibonacci sequences, generalized by variable seeds, model durations in physical movements.
- Self-similar patterns, linked to the golden ratio, emerge in the sub-phase durations of gestures.
- Understanding these patterns is crucial for analyzing and automating cyclic human movements.
Purpose of the Study:
- To provide a mathematical framework for the automatic generation of Fibonacci sequence-based, self-similar patterns in human movements.
- To explore the cognitive underpinnings of motor learning and adaptation related to these patterns.
- To extend gait characterization to gestures in sports like swimming and tennis.
Main Methods:
- Utilizing generalized Fibonacci sequences with variable seeds to represent sub-phase durations.
- Analyzing self-similar patterns characterized by the golden ratio in movement sequences.
- Applying mathematical modeling to understand the automatic generation process of these patterns.
- Illustrating the approach with data from walking and tennis playing.
Main Results:
- Identified hidden Fibonacci sequence-based and self-similar patterns in the temporal design of human gestures.
- Demonstrated that these patterns exhibit harmonic and aesthetic qualities, simplifying temporal design.
- Established a mathematical understanding of the automatic generation of these patterns in cyclic movements.
- Validated the effectiveness of the proposed approach using real-world data from walking and tennis.
Conclusions:
- Generalized Fibonacci sequences and self-similar patterns offer a novel approach to characterizing human movement.
- The mathematical framework provides insights into the cognitive factors influencing motor learning and adaptation.
- This research paves the way for a deeper understanding and potential automation of complex physical gestures.
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