I've always found what happens in the third dimension weird. A 0-dimensional space needs up to: 1 color. A 1-dimensional space needs up to: 2 colors. A 2-dim

I've always found what happens in the third dimension weird. A 0-dimensional space needs up to: 1 color. A 1-dimensional space needs up to: 2 colors. A 2-dimensional space needs up to: 4 colors. A 3-dimensional space needs up to: ∞ colors. I can easily picture why a 3D space has no limit to the number of colors (personally I always imagine color blocks hanging in space connected to every other color block by bendable wires), but I don't quite understand why the pattern is that way.