Speaking of the richness of low-information states... there's also a kind of opposite to this: a lack of richness of high-information states. Consider a beam of light entering a liquid like water. There's a great deal of noise and variation in the positions of the water molecules, but due to the low-dimension (3) of the space and the high density of the material, there is an inevitable kind of 'regularity' that makes the material act on aggregate as though it were simply a region of simple refraction, rather than a complex superposition of billions of electromagnetic interactions.
Actually, this is probably captured by the idea of randomness.
Actually, this is probably captured by the idea of randomness.