Disclaimer: I am not a professional 3D printer, so I'm not really familiar with how 3D printing works.
I was thinking about trying to make a real life model of the atomic orbitals, to clearly see how the orbitals are really shaped. I thought about trying to 3D print a block, made up of colored transparent "ink", in such a way that the darkness of the color at a point in the block should be proportional to the ψ2 value (probability of the electron cloud). This would print a block in which high density areas are darker than light intensity areas.
My question is, would it be possible to design an algorithm to print a specific darkness of ink at a specific location based on the computed value of ψ2, which is obtained by solving Schrödinger's Equation. Also, would it be possible to have this fullfilled at a reasonable price to be afforded by a regular customer, such as an engineering employee?
3d printing a gradient like that will take:
1) A program capable of graphing color into your 3D model 2) A 3D printer capable of printing multiple colors (multi nozzle 3D printers) 3) Some way to convert that density function to a change in color.
There are certain types of files called .3mf files that can hold different color information- but I thinking relating the electron density to a change in color may be rather difficult (if possible at all).
I think a better bet is to go with the 3D probability map of a 2D Image, as suggested by Gumbo.
I have come across a neat little project that is half of what you are looking for. These are mathematically accurate, 3D printed atomic orbitals (graphed with their Schrodinger Equations). Link Here: https://pubs.acs.org/doi/abs/10.1021/acs.jchemed.6b00293