What exactly is this small puffer fish doing and how did it manage to accomplish such a feat?
A tiny Japanese puffer fish creates a grand sand sculpture on the featureless seabed by using his fins to dig furrows. He uses this to attract the attention of passing females.
  
  
  Why do puffer fish build sandcastles? (BBC)
  





  Further observation revealed that this “mysterious circle” was not just there to make the ocean floor look pretty. Attracted by the grooves and ridges, female puffer fish would find their way along the dark seabed to the male puffer fish where they would mate and lay eggs in the center of the circle. In fact, the scientists observed that the more ridges the circle contained, the more likely it was that the female would mate with the male. The little sea shells weren’t just in vain either. The observers believe that they serve as vital nutrients to the eggs as they hatch, and to the newborns.
  
  
  http://www.spoon-tamago.com/2012/09/18/deep-sea-mystery-circle-love-story/
  


Here is the source of the video:


Puffer Fish Constructs A Masterpiece of Love - BBC Earth (YouTube)




The following papers analyse said structures and the ethology in more depth:


  We report that male pufferfishes (Torquigener sp., Tetraodontidae) constructed large geometric circular structures on the seabed that played an important role in female mate choice. Males dug valleys at various angles in a radial direction, constructing nests surrounded by radially aligned peaks and valleys. Furthermore, they created irregular patterns in the nest comprising fine sand particles. The circular structure not only influences female mate choice but also functions to gather fine sand particles in nests, which are important in female mate choice. Strangely enough, the males never reuse the nest, always constructing a new circular structure at the huge cost of construction. This is because the valleys may not contain sufficient fine sand particles for multiple reproductive cycles.
  
  
  Role of Huge Geometric Circular Structures in the Reproduction of a Marine Pufferfish (2013)
  





  Here, we examined the process of the outer ring construction, and extracted the ‘rules’ followed by the pufferfish. During construction, the pufferfish repeatedly excavates ditches from the outside in. Generally, excavation starts at lower positions, and occurs in straight lines... A simulation program based on these data successfully reproduced the circle pattern, suggesting that the complex circle structure can be created by the repetition of simple actions by the pufferfish.
  
  
  Simple rules for construction of a geometric nest structure by pufferfish (2018)