It has never occurred to me that it might be possible for an octopus to dream. And I have certainly never seen a video of it.
But from what I gather here, few people have.
The fact that this is possible, and that an octopus might have vivid and impactful dreams too, reminds me of reading Pilgrim at Tinker Creek, (Amazon) By: Annie Dillard.
Dillard highlights the wonder of it all in a poetic way, for example:
Of all known forms of life, only about ten percent are still living today. All other forms—fantastic plants, ordinary plants, living animals with unimaginably various wings, tails, teeth, brains—are utterly and forever gone. That is a great many forms that have been created. Multiplying ten times the number of living forms today yields a profusion that is quite beyond what I consider thinkable. Why so many forms? Why not just that one hydrogen atom? The creator goes off on one wild, specific tangent after another, or millions simultaneously, with an exuberance that would seem to be unwarranted, and with an abandoned energy sprung from an unfathomable font. What is going on here? The point of the dragonfly’s terrible lip, the giant water bug, birdsong, or the beautiful dazzle and flash of sunlighted minnows, is not that it all fits together like clockwork—for it doesn’t, particularly, not even inside the goldfish bowl—but that it all flows so freely wild, like the creek, that it all surges in such a free, fringed tangle. Freedom is the world’s water and weather, the world’s nourishment freely given, its soil and sap: and the creator loves pizzazz.