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Wild animals construct various types of structures that are adaptive to their life and reproduction. For example, termites that inhabit the African savanna use soil to construct a huge mound that reaches 10 m in height; they produce hollows and holes in these mounds to allow air ventilation, thereby keeping the internal temperature constant1. In addition, prairie dogs inhabiting the North American prairie dig vertically and horizontally extending burrows in the ground that they use for shelter and rearing offspring; these burrows have multiple entrances, some of which are chimney-shaped to improve ventilation efficiency2. In the field of biomimetics, researchers apply the principles of animal-created structures in applications useful to humans3.The white-spotted pufferfish Torquigener albomaculosus (Pisces: Tetraodontidae) is a relatively small species that grows to ~10 cm in total total length (Fig. 1). Male T. albomaculosus individuals construct an intricate geometric circular structure, known as the “mystery circle,” with a diameter of 2 m in the sand of the seabed;4 the discovery of these structures has fascinated researchers and the general public worldwide. The male pufferfish digs the sand on the seabed with its fins and body while swimming straight ahead toward the centre from different directions, and a circular structure composed of radially aligned peaks and valleys was constructed. Finally, the male creates a maze-like pattern by flapping its anal fin on the bottom of the central zone4. Thus, the male completes the circular structure by himself. Furthermore, we discovered that the earliest stage of the mystery circle is composed of dozens of irregular depressions, which might function as landmarks for the formation of the radial patterns5. By accumulating observations of pufferfish behaviour, we were able to conduct a computer simulation including the swimming trajectory of the pufferfish extracted from video images wherein they constructed the circular structure. This simulation revealed that an elaborate circular geometric pattern is inevitably formed if the pufferfish repeats the digging behavior on the seabed using simple rules6. We also observed the reproductive behaviour of the pufferfish and found that they consistently breed in a semilunar cycle from spring to summer. Each male constructs a mystery circle and spawns with multiple females on the nest, and the male cares for the eggs alone until they hatch. Some of the elements of the circular structure, i.e., its size, symmetry, ornaments, and maze-like pattern, might be important factors in terms of female mate choice4,7.Fig. 1The white-spotted pufferfish Torquigener albomaculosus. Lateral view of a male (a), and male digging behaviour on the seabed while rolling up fine sand particles (b).Full size imageAlthough data on the reproductive ecology and circle-construction behaviour of these pufferfish have been collected, many questions remain. Our interdisciplinary research currently has two themes: (i) theoretical studies on the logic of 3D-structure formation of the circular structure and (ii) ethological studies on the relationship between female mate choice and the features of the structure. To advance these studies, it is essential to collect quantitative data on the circular structure. Thus, we reconstructed 3D models of six completed mystery circles using a “structure from motion” (SfM) algorithm (Fig. 2).Fig. 2“Mystery circle” constructed by a white-spotted pufferfish (Torquigener albomaculosus). 3D model displayed on a computer (a), one of the video frames used to reconstruct the 3D model (b), and a Styrofoam model output in full size created using a 3D printer and the 3D data (c) for a specific mystery circle 20160615_K13.Full size imageOn the other hand, the mystery circle constructed by the pufferfish may have potential applications in biomimetics similar to the structures constructed by termites and prairie dogs. To support the importance of its structural characteristics, it has been observed that the water passing through the valley upstream always gathers in the center of the structure, regardless of the direction of water flow4. Furthermore, particle size analysis of the sand forming the mystery circle has revealed that it has the function of extracting fine-grained sand particles from the valleys arranged radially to the outside and directing them to the center (Kawase, in prep.). The field of computational fluid dynamics, which makes full use of fluid dynamics technology, engineering knowledge, and computers, will logically clarify the characteristics of the 3D structure of the mystery circle we have reconstructed here. Shameem et al. reconstructed a 3D model of a mystery circle to explore the flow features with 2D computational fluid dynamic simulations8. Since our model has already been quantified as 3D data, computational fluid analysis can be immediately performed using this data, and the structural features of the mystery circle are expected to be applied in a wide range of fields, such as architecture and engineering, via biomimetics. More

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