Can the process of generating a password based on the transformation of random 3D data into a 2D data chain have better entropy than other methods of generating 2D random data chains?
It sounds like you're describing one of two things:
A process in which data is generated somewhat randomly, but constrained by being mapped to a 3D structure with certain properties. If so, it will necessarily be less random than a method that is not constrained in that way.
A process in which completely random data happens to be projected into 3 dimensions. If so, the initial projection is immaterial to the underlying entropy of the data ... but any subsequent transformation (converting to raw 2D equivalents, using base64, etc.) could do nothing to improve the entropy. And that transformation might make it worse if it has non-random components.
Either way, the process you're describing would be no better than random data - and could be worse.