A lot of animal blue is a structural trick. Pigments that stay blue are chemically awkward, so birds, butterflies, and cephalopods often build a surface that sorts light instead of a dye that absorbs it. The ring octopus is in that company. The iridophores in the rings are stacks of thin reflecting plates. Light bouncing off successive layers interferes with itself, and the wavelength that comes back to the eye is blue to blue-green.
Interference color shifts a little with angle, which is why the rings can look lit from inside rather than painted on. Move your head and the blue seems to brighten or cool. The animal does not spend metabolic effort synthesizing a blue dye and then pushing it to the skin. It spends the effort on the muscles that hide and reveal a structure that is already there. Between flashes, the rings can be so faint that a resting animal looks like any other small brown octopus on sand.
That economy matters. A warning signal that is off most of the time lets the animal keep the other half of its strategy, which is camouflage. Chromatophores and skin texture hide it while it hunts and rests. The rings are reserved for the moment camouflage has failed. An animal that was brilliant blue all day would be easy to find, and would also teach predators to ignore the signal by making it ordinary. The switch is the point.
Stand where the sun is on the water and the effect is stronger. The reflectors need light to throw back. In a dim crevice the same animal is mostly a softness and a shadow, which is how it prefers to be found, if it is found at all.