[chillocrat]

I'm looking for a chemical formula for an elastic material similar to memory foam. Let's say I have a 12in x 12in x 36in (width x height x length) block of said material — the height needs to be able to squeeze down to 5 inches so that the final dimensions are 12inx 5in x 36in. It needs to be durable enough to resist scratches (unlike regular foam), and dense enough when compressed to 5 inches that I wouldn't be able to poke my index finger into it more than 1 inch deep (unlike memory foam). It needs to be non-toxic.

[Enthalpy]

Your needs look reasonable. Non-toxic is good to know but won't rule many elastomers out.

My suggestion is that you query an elastomer company. Dozens of plain elastomers and their foams (or even a tyre) look still possible based on you description, and the hardness is very widely adjusted for one single chemical composition, by the degree of cross-linking among others. That's a specialist job for a specialist company. And don't get afraid by qualitative answers: numbers and equations have a limited usefulness with rubbers.

Do you have some more constraints?

• Shall it give the deformation energy back (only natural rubber excels at it) or absorb it (PU does, and most foams too)?
• Do you accept a long-lasting deformation after a prolonged compression?
• Heat, cold? Both are difficult for rubbers.
• Prolonged exposition to sunlight? To UV? To ozone? Ionizing rays?
• Warm water for long? Chemicals? Operation in vacuum?
• What force shall compress your brick from 12in to 5in?

Try not to exaggerate these constraints, because some rubbers are really expensive and your brick is big.

[Enthalpy]

Maybe cork could fulfill your requirements, depending on the pressure that compresses it from 12in to 5in. At least it's nontoxic ad cheap.