Modelling and Analysis of Pufferfish (Torquigener albomaculosus) Circular Nest on Seafloor

Year 2023, Volume: 12 Issue: 4, 473 - 482, 31.12.2023

Mehmet Cem Çatalbaş

https://doi.org/10.33714/masteb.1305023

Abstract

This study analyzed the structural features of the circular structures built by the male pufferfish (Torquigener albomaculosus) on the seafloor. This impressive circular structure which is built by male pufferfish exists in different depths and sizes on the seafloor. One of the objectives for the male pufferfish constructing these circular structures is to influence the opposite sex. The morphological features of these circular structures built on the sea floor were analyzed mathematically. This analytical study was performed using photographs received from the sea floor as well as the ratios of circular formations discovered in this context. During the image analysis, the histogram equalization method was used to improve the visuals and reveal the patterns of circular structures. The Hough transform method, which is commonly used in the determination of circular structures, was used in the process of precisely determining the dimensions of the obtained circular structures. The circle size ratios obtained from the images and the circular structure dimension ratios obtained from the observation were examined. When the ratio analysis results from 2 images and 6 observation data were examined, it was observed that significant traces of the golden ratio were seen in these nested circular structures. According to this study’s analysis of the pufferfish nest, which demonstrated proper development, the percentage difference between the golden ratio and the radius of the circular structures was determined to be as low as 0.185%. Additionally, these circular constructions were recreated in 3D while preserving their proportions, and their hydrostatic pressure characteristics were analyzed depending on their actual depths on the seafloor.

Keywords

Animal behaviour, Shape analysis, Mathematical modelling, Torquigener albomaculosus, Golden ratio, Bio-inspired

Ethical Statement

For this type of study, formal consent is not required.

References

• Akhtaruzzaman, M., & Shafie, A. A. (2011). Geometrical substantiation of Phi, the golden ratio and the baroque of nature, architecture, design and engineering. International Journal of Arts, 1(1), 1-22. https://doi.org/10.5923/j.arts.20110101.01
• Aksoy, A. G. (2016). Al-Khwarizmı and the Hermeneutic Circle: Reflections on a Trip to Samarkand. Journal of Humanistic Mathematics, 6(2), 114-127. https://doi.org/10.5642/jhummath.201602.09
• Bartlett, C. (2019). Nautilus spirals and the meta-golden ratio chi. Nexus Network Journal, 21(3), 641-656.
• Belluscio, V., Iosa, M., Vannozzi, G., Paravati, S., & Peppe, A. (2021). Auditory Cue based on the Golden ratio can improve gait patterns in people with Parkinson’s disease. Sensors, 21(3), 911. https://doi.org/10.3390/s21030911
• Catalbas, M. C., & Gulten, A. (2022). Pufferfish Optimization Algorithm: A Bioinspired Optimizer. In M. S. Manshahia, V. Kharchenko, E. Munapo, J. J. Thomas & P. Vasant (Eds.), Handbook of Intelligent Computing and Optimization for Sustainable Development (pp. 461-485). Scrivener Publishing LLC, Wiley.
• Ciucurel, C., Georgescu, L., & Iconaru, E. I. (2018). ECG response to submaximal exercise from the perspective of Golden Ratio harmonic rhythm. Biomedical Signal Processing and Control, 40, 156-162. https://doi.org/10.1016/j.bspc.2017.09.018
• Dhal, K. G., Das, A., Ray, S., Gálvez, J., & Das, S. (2021). Histogram equalization variants as optimization problems: A review. Archives of Computational Methods in Engineering, 28(3), 1471-1496. https://doi.org/10.1007/s11831-020-09425-1
• Fletcher, R. (2006). The golden section. Nexus Network Journal, 8(1), 67-89. https://doi.org/10.1007/s00004-006-0004-z
• Henein, M. Y., Zhao, Y., Nicoll, R., Sun, L., Khir, A. W., Franklin, K., & Lindqvist, P. (2011). The human heart: Application of the golden ratio and angle. International Journal of Cardiology, 150(3), 239-242. https://doi.org/10.1016/j.ijcard.2011.05.094
• Herrmann, B. (2018). Visibility in a pure model of golden spiral phyllotaxis. Mathematical Biosciences, 301, 185-189. https://doi.org/10.1016/j.mbs.2018.05.003
• Iosa, M., Morone, G., & Paolucci, S. (2018). Phi in physiology, psychology and biomechanics: The golden ratio between myth and science. Biosystems, 165, 31-39. https://doi.org/10.1016/j.biosystems.2018.01.001
• Kawase, H., Mizuuchi, R., Shin, H., Kitajima, Y., Hosoda, K., Shimizu, M., Iwai, D., & Kondo, S. (2017). Discovery of an earliest-stage “Mystery Circle” and development of the structure constructed by pufferfish, Torquigener albomaculosus (Pisces: Tetraodontidae). Fishes, 2(3), 14. https://doi.org/10.3390/fishes2030014
• Kawase, H., Okata, Y., & Ito, K. (2013). Role of huge geometric circular structures in the reproduction of a marine pufferfish. Scientific Reports, 3(1), 2106. https://doi.org/10.1038/srep02106
• Kawase, H., Okata, Y., Ito, K., & Ida, A. (2014). Spawning behavior and paternal egg care in a circular structure constructed by pufferfish, Torquigener albomaculosus (Pisces: Tetraodontidae). Bulletin of Marine Science, 91(1), 33-43. https://doi.org/10.5343/bms.2014.1055
• Livio, M. (2008). The golden ratio: The story of phi, the world’s most astonishing number. Broadway Books.
• Lüttge, U., & Souza, G. M. (2019). The Golden Section and beauty in nature: The perfection of symmetry and the charm of asymmetry. Progress in Biophysics and Molecular Biology, 146, 98-103. https://doi.org/10.1016/j.pbiomolbio.2018.12.008
• Matsuura, K. (2015). A new pufferfish of the genus Torquigener that builds “mystery circles” on sandy bottoms in the Ryukyu Islands, Japan (Actinopterygii: Tetraodontiformes: Tetraodontidae). Ichthyological Research, 62(2), 207-212. https://doi.org/10.1007/s10228-014-0428-5
• Meisner, G. B. (2018). The Golden Ratio: The Divine Beauty of Mathematics. Race Point Publishing.
• Mizuuchi, R., Kawase, H., Shin, H., Iwai, D., & Kondo, S. (2018). Simple rules for construction of a geometric nest structure by pufferfish. Scientific Reports, 8(1), 12366. https://doi.org/10.1038/s41598-018-30857-0
• Nematollahi, A. F., Rahiminejad, A., & Vahidi, B. (2020). A novel meta-heuristic optimization method based on golden ratio in nature. Soft Computing, 24(2), 1117-1151. https://doi.org/10.1007/s00500-019-03949-w
• Schaedelin, F. C., & Taborsky, M. (2009). Extended phenotypes as signals. Biological Reviews, 84(2), 293-313. https://doi.org/10.1111/j.1469-185x.2008.00075.x,
• Strauss, S., Lempe, J., Prusinkiewicz, P., Tsiantis, M., & Smith, R. S. (2020). Phyllotaxis: Is the golden angle optimal for light capture?. New Phytologist, 225(1), 499-510. https://doi.org/10.1111/nph.16040
• Sugimoto, T. (2021). Inducing the symmetries out of the Complexity: The Kepler Triangle and its kin as a model problem. In G. Darvas (Ed.), Complex symmetries (pp. 71-78). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-88059-0_7
• Yalta, K., Ozturk, S., & Yetkin, E. (2016). Golden Ratio and the heart: A review of divine aesthetics. International Journal of Cardiology, 214, 107-112. https://doi.org/10.1016/j.ijcard.2016.03.166