Costello the octopus was napping while stuck to the glass of his tank at the Rockefeller University in New York. He snoozed quietly for half an hour, and then entered a more active sleep stage, his skin cycling through colors and textures used for camouflage — typical behavior for a cephalopod.

But soon things became strange.

A minute later, Costello scuttled along the glass toward his tank’s sandy bottom, curling his arms over his body. Then he spun like a writhing cyclone. Finally, Costello swooped down and clouded half of his tank with ink. As the tank’s filtration system cleared the ink, Eric Angel Ramos, a marine scientist, noticed that Costello was grasping a pipe with unusual intensity, “looking like he was trying to kill it,” he said.

“This was not a normal octopus behavior,” said Dr. Ramos, who is now at the University of Vermont. It’s not clear when or if Costello woke up during the episode, Dr. Ramos said. But afterward, Costello returned to normal, eating and later playing with his toys.

“We were completely dumbfounded,” said Marcelo O. Magnasco, a biophysicist at Rockefeller. Perhaps Costello was having a nightmare, he and a team of researchers speculated. They shared this idea and other possible explanations in a study uploaded this month to the bioRxiv website. It has yet to be formally reviewed by other scientists.