The caterpillar wraps himself in a chrysalis or cocoon and seems to die.
Then the chrysalis or cocoon splits and a moth or butterfly emerges.  
Then the wings open, and the creature who once crawled in the dirt now
flies, is spectacularly beautiful, and no longer eats, or only sips nectar.

Are Egyptian mummies based on this observation?

Many religions, all Mystery Schools, and the observation of mystics reflect this same opinion about the life and death of human beings.