Video captured by Rebecca Otey (via YouTube) at the Butterfly Pavilion in Colorado seems to suggest that perhaps octopuses dream in their sleep:
Although it is not clear whether octopuses really are dreaming when they change colors in their sleep, researchers at the World Science Festival in 2011 discussed work studying changes in brain activity of animals during sleep compared to wakefulness to gauge whether they may be dreaming:
Categories: Intelligence and Neuroscience, Ocean Life, Pets
Tags: color, dream, Octopus, octopuses, sleep