The sense that the self exists somewhere close to the brain or heart is an intuitive one for humans. It also seems to apply to most of the animals we regularly encounter, even when they can regrow parts of their body. When a crayfish gets into a tight spot and loses one of its claws, the part of the crayfish with the head will regrow the lost claw, but the claw won’t regrow a body and head.
For many animals, though, there is no such essential center of the organism. When a flatworm gets its tail cut off, both the tail and head will fill in the missing parts and make two whole flatworms that are clones of each other. Its body is arranged such that there isn’t a single part of the animal that can be identified as the core.
Here is a bit of footage taken by Stephanie Spielman, an undergraduate in Casey Dunn and Gary Wessel’s seminar on the evolution of multicellularity at Brown University. The clip features the flatworm Dugesia tigrina swimming around the Dunn lab. It is released under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 license. The crawfish video is from Day at the River (1928), a video from DeVry School Films, Inc., which is under public domain.