This sounds a lot like synesthesia. Not the association of colors and sounds, but visual-mathematical synesthesia. There are people, like you, that can do arithmetic simply by looking at number-boards that float in the field of vision, like a visual slide-rule.

While I conceptualize differently than you, I do play the "morphing shapes/structures game," falling asleep, but it's in black and white. Also, I float around objects on all axises, like floating around the exterior of a spaceship...