# Complexity, Regularity and Non-Linear Behavior in Human Eye Movements: Analyzing the Dynamics of Gaze in Virtual Sailing Programs

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{TM}) created by Applied Sciences Laboratories (ASL

^{®}). The eye tracker is a head-mounted, monocular eye-tracking device that computes the point of gaze within a scene by calculating the vector (angle and distance) between the individual’s pupil and cornea. Gaze behavior data were collected at 30 frames per second (30 Hz).

^{®}simulator (Figure 1). This session consisted of a three-minute free navigation session and a guided navigation session, which included three minutes of directive audio that the sailors were required to follow.

#### FuzzyEn and DFA Analysis

^{2}

_{p}). Pearson correlation coefficients were estimated to analyze the link between the complexity of visual behavior and a sailor’s ranking and experience.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Acknowledgments

^{®}simulator, for all of the help they provided.

## Conflicts of Interest

## References

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**Figure 2.**Low and high values of detrended fluctuation analysis (DFA) (

**A**) and fuzzy entropy (FuzzyEn) (

**B**) selected from the sample.

**Figure 3.**Eye movements of one sailor during the race, and scene with stimuli (randomly selected from the sample).

**Figure 4.**FuzzyEn values for eye positions and velocity at the first and second regatta start. * Significant differences in FuzzyEn values between regularity of eye position and velocity.

**Figure 5.**Correlations found between the regularity—FuzzyEn—of the eye movements and the age of sailors.

**Figure 6.**DFA alpha values in eye positions and velocity at the first and second regatta start. * Significant differences (p ≤ 0.05) in DFA alpha values between the complexity of eye position and velocity.

**Figure 7.**Correlation found between the regularity—alpha DFA values—of the eye movements and the age of sailors.

**Table 1.**Effects of the sailors’ ranking position and experience, as well as the spatial axis of eye movement, on the regularity of eye movements (FuzzyEn).

Ranking | Years’ Experience | ||||||||
---|---|---|---|---|---|---|---|---|---|

Race | Axis | FuzzyEn | F(_{1,29}) | p | η^{2}_{p} | F(_{1,29}) | p | η^{2}_{p} | |

Eye position | 1st | X | 0.32 ± 0.08 | 0.523 | 0.599 | 0.037 | 0.524 | 0.784 | 0.120 |

1st | Y | 0.31 ± 0.07 | 0.541 | 0.588 | 0.039 | 0.442 | 0.843 | 0.103 | |

2nd | X | 0.33 ± 0.07 | 0.838 | 0.443 | 0.058 | 1.874 | 0.129 | 0.328 | |

2nd | Y | 0.34 ± 0.11 | 0.204 | 0.817 | 0.015 | 0.272 | 0.945 | 0.066 | |

Eye velocity | 1st | X | 0.69 ± 0.12 | 0.896 | 0.420 | 0.062 | 1.133 | 0.375 | 0.228 |

1st | Y | 0.69 ± 0.13 | 0.937 | 0.404 | 0.065 | 0.427 | 0.853 | 0.100 | |

2nd | X | 0.69 ± 0.13 | 1.110 | 0.344 | 0.076 | 0.702 | 0.651 | 0.155 | |

2nd | Y | 0.69 ± 0.15 | 0.229 | 0.797 | 0.017 | 0.368 | 0.892 | 0.088 |

_{1,29}) = F-value (degrees of freedom); p-value ≤ 0.05; η

^{2}

_{p}= partial eta squared -effect size-.

**Table 2.**Effects of the sailors’ ranking position, experience and of the spatial axis of eye movement on the complexity of eye movements (DFA).

Ranking | Experience | ||||||||
---|---|---|---|---|---|---|---|---|---|

Race | Axis | DFA | F(_{1,29}) | p | η^{2}_{p} | F(_{1,29}) | p | η^{2}_{p} | |

Eye position | 1st | X | 0.96 ± 0.09 | 1.722 | 0.198 | 0.113 | 1.166 | 0.342 | 0.119 |

1st | Y | 0.96 ± 0.09 | 2.494 | 0.101 | 0.156 | 2.335 | 0.097 | 0.212 | |

2nd | X | 0.93 ± 0.12 | 0.859 | 0.435 | 0.060 | 0.269 | 0.847 | 0.030 | |

2nd | Y | 0.93 ± 0.13 | 1.015 | 0.376 | 0.070 | 1.294 | 0.297 | 0.130 | |

Eye velocity | 1st | X | 0.25 ± 0.03 | 1.794 | 0.186 | 0.117 | 1.140 | 0.352 | 0.116 |

1st | Y | 0.24 ± 0.04 | 2.971 | 0.068 | 0.180 | 2.308 | 0.100 | 0.210 | |

2nd | X | 0.20 ± 0.04 | 1.339 | 0.279 | 0.090 | 0.947 | 0.432 | 0.098 | |

2nd | Y | 0.20 ± 0.04 | 0.094 | 0.911 | 0.007 | 0.834 | 0.487 | 0.088 |

_{1,29}) = F-value (degrees of freedom); p-value ≤ 0.05; η

^{2}

_{p}= partial eta squared -effect size-.

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**MDPI and ACS Style**

Menayo, R.; Manzanares, A.; Segado, F.
Complexity, Regularity and Non-Linear Behavior in Human Eye Movements: Analyzing the Dynamics of Gaze in Virtual Sailing Programs. *Symmetry* **2018**, *10*, 528.
https://doi.org/10.3390/sym10100528

**AMA Style**

Menayo R, Manzanares A, Segado F.
Complexity, Regularity and Non-Linear Behavior in Human Eye Movements: Analyzing the Dynamics of Gaze in Virtual Sailing Programs. *Symmetry*. 2018; 10(10):528.
https://doi.org/10.3390/sym10100528

**Chicago/Turabian Style**

Menayo, Ruperto, Aarón Manzanares, and Francisco Segado.
2018. "Complexity, Regularity and Non-Linear Behavior in Human Eye Movements: Analyzing the Dynamics of Gaze in Virtual Sailing Programs" *Symmetry* 10, no. 10: 528.
https://doi.org/10.3390/sym10100528