I'm thinking of some sort of machine the size of a house or factory building which produces nutrient paste/cubes/wafers/pills using some of the basic materials/chemicals and energy which are required to run a farm today. Which materials would be required to sustain such a system?
Nanotechnology and power.
Advanced nanotechnology could be used to build the necessary molecules and even duplicate natural foods quite well. But, do so with an engineered purpose and be orders of magnitude smaller than a natural ecosystem.
To run it, you need power. Input energy to drive the machinery. Since it builds up tissue much faster than natural plants, it needs more power, faster. Since it is smaller than natural plants it can’t devote expansive areas to solar collectors.
As for “materials”, nanotech based on what we see in cells will use the same kinds of atoms. So, it is made from the same stuff that it is manipulating.
More novel tech might make use of catalysts that use the full variety of existing elements, including platinum group metals and rare earth metals. These would be needed in smaller amounts than current tech, but greater than what’s found in organic material. So, besides taking what it needs from the compost it’s reforming into food, it need supplements from carefully sourced minerals.