## 3 Results and Discussion
The Shannon Entropy values calculated on the same data as the FDs, _i.e._, the trajectories displayed in Figure 4 are shown in Table 3. There was no difference between the entropy calculated on the X or the Y values. It is noteworthy the large difference between the entropy of C3 and those of C1 or C2, which only differed slightly from each other (Table 3). This seems to indicate that the Shannon entropy decreases with increasing perturbation of the fish: tagging having only a minimal and possibly non-significant effect, but the presence of the contaminant drastically diminished the entropy of the system by an entire unit. The permutation Entropy values calculated for the three experimental cases are also shown in Table 3. The results differ very slightly for X and Y signals and, in contrast to the results obtained using Shannon Entropy, the three analysed cases presented very similar permutation entropy values, although, in agreement with it, the permutation entropy values for C3 were smaller than for C1 and C2. Technically, the method presented here demands a relatively large computation capability, particularly for the image processing step, which is of course susceptible of improvement. It must also be kept in mind on one hand that the analysis of the fish clusters trajectories does not depend on an image, they can \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Case** & \multicolumn{3}{c}{**Sliding Window Length**} \\ \cline{2-4}  & **320** & **640** & **1280** \\ \hline
**C1** & 2.1415 & 2.2624 & 2.4420 \\
**C2** & 2.0449 & 1.9188 & 2.1043 \\
**C3** & 2.4752 & 2.4618 & 2.5207 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Medians of the Fractal Dimensions Obtained for Each Sliding Window Lenght (320, 640 and 1280) in C1, C2, and C3. Note how close are the medians for C3. Figure 5: Comparison of the three fractal dimension algorithms (Higuchi, blue lines; Katz, green lines and Katz-Castiglioni, red lines) evolution for each case signal (X, broken lines; and Y, full lines) and for each window length (left column 320, middle column 640 and right column 1280) for C1 (top row), C2 (middle row) and C3 (lower row). In each graphic the vertical 0Y axis is the fractal dimension of the cluster’s centroids and the horizontal 0X axis is the evolution of the fractal dimension per sliding window length. As mentioned in the text, the fractal dimension for the Katz algorithm gave a value of 1 regardless of the signal case or the window length. also be obtained from echo-sounds or infrared images and, on the other hand, that the methodology is not exclusive for fish and that with some modification may be applicable to other species. Of the tested methodologies, two of them, namely those based on the analysis of the Katz-Castiglioni FD and the Shannon entropy of the trajectories have been shown to be useful tools for non-invasive identification and quantification of changes of fish responses due to a highly relevant environmental \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{2}{l}{**Shannon Entropy Values**} & \multicolumn{2}{l}{**Permutation Entropy Values**} \\ \cline{2-5}  & **X Coordinate** & **Y Coordinate** & **X Coordinate** & **Y Coordinate** \\ \hline
**C1** & 6.3016 & 6.3016 & 3.0881 & 3.0950 \\
**C2** & 6.2861 & 6.2861 & 3.1049 & 3.1250 \\
**C3** & 5.3628 & 5.3628 & 3.0413 & 3.0618 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Shannon Entropy Values Calculated for the X and Y Coordinates for C1, C2, and C3. Figure 6: Boxplot representation of the fractal dimension data obtained by the Katz-Castiglioni algorithm, for each case (C1 upper, C2 middle and C3 lower row) and window length (320 left, 640 middle and 1280 right column). The upper and lower lines in each box represent the 75 th and 25 th percentile of the sample data respectively. The distance between those lines is the inter-quartile range and the red line inside the box is the sample data median.