Master Thesis

Title: “Characterization of Fractal Fluctuations in a Complex Motor Performance”


  • Nantes Communication and Cybernetics Research Institute (IRCCyN), UMR 6597 CNRS, Ecole Centrale de Nantes – Nantes, FRANCE
  • Laboratory Motricity, Interactions, Performance (MIP), EA 4334, UFR STAPS, University of Nantes – Nantes, FRANCE


Fractals, in nature, can be found in geometrical shapes, real-world physical entities, dynamics of biological systems and several types of signals. Many research areas, from physics to image and acoustic analysis, as well as the study of chemical processes and biological dynamics, exploit today the models offered by multifractal analysis. Within the scope of Signal Processing, many natural irregular signals can be analysed as fractal processes. The main advantage offered by this approach is the possibility to describe very complex natural phenomena by using a small set of parameters. In these terms, the detection of signals with fractal features in real-world realizations might reveal to be of great interest. Moreover, fractal models have revealed to be very versatile tools and their mathematical formalization has been impressively developed in the last decades.

When the irregularity of the signal is supposed to be directly linked to relevant information about the studied phenomenon (even if this irregularity often emerges as the result of very complex interactions among a large number of elements), the identification of a multifractal behaviour of the signal may reveal to be a very efficient analysis tool. For instance, when studying the expressions of human motor behaviour, irregularity is supposed to play a functional role in the maintenance and adaptability of systems. It has been shown that a healthy system autonomously organizes itself with fractal-like features, which can be found in many physiological recordings like heartbeat rate, gait fluctuations and manual coordination tasks.

For my MSc thesis research work, we studied a very simple motor task based on the execution of repeated wrist oscillations to be performed by pairs of subjects. The goal was that of acting together, either in In-Phase or Anti-Phase coordination. The selected subjects were characterized by different level of anxiety and the underlying idea was that this feature affected the execution of the motor performance in terms of fractal characterizations. During their movements, the interpersonal delay for each pair (called Relative Phase, RP) was recorded and analysed by means of multifractal analysis.

The first objective of this work consisted in verifying the presence of fractal features in the RP data. Considering this kind of experiment, it was the first time that such a case was studied. Three different techniques (the Box-Counting Method , the Regularization Dimension and the Spectral Analysis) were employed to evaluate the fractal-like characterization of RP data. By comparing the experimental outcomes with reference data found in the literature, the presence of fractal-like characterizations in the RP data was successfully assessed.

The second objective of this work consisted in checking whether the different level of anxiety of the studied pairs of participants affected or not the motor performance. To this purpose, the Analysis of Variance (ANOVA) statistical test was employed. The population was quite small (only 18 people). Despite this, however, the effect of anxiety emerged as a determinant factor in the motor task execution.

For future work, the following methodological limits of our study were depicted:

  • the type of motor task could be adjusted so as to give more importance to the anxiety feature;
  • taking longer recordings could allow to collect more interesting data;
  • enlarging the population was deemed as a key point to produce more reliable statistics.

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