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Well, you would need a source of fresh water and growing medium, as well as of course the carbon input from the air. You’d need to start with a substantial input to the system, either eating for weeks while fertilizing the first batch of plants, or start with fertilizer or natural soil to kick start the cycle. But if properly designed yes, it’d be entirely possible.
And, it is possible to produce nutrients directly from human waste but it will never give you enough calories to sustain the system, growing food the plants take in sunlight which is what actually provides you with energy, the rest is just cycling around different forms of matter.
