When Astrid enters the battlefield, its first ability and Samwise Gamgee trigger.
Resolve the Astrid trigger, creating two Clue, two Food and two Treasure tokens.
Resolve the Samwise Gamgee trigger, creating two Clue, two Food and two Treasure tokens.
Activate Phyrexian Altar by sacrificing Astrid, adding .
Activate Samwise Gamgee by sacrificing three Foods, returning Astrid from your graveyard to your hand.
Activate a Treasure by tapping and sacrificing it, adding 1.
Repeat.
This brilliant loop harnesses the synergistic token-doubling of Peregrin Took and the sweeping replacement effects of Academy Manufactor to turn a single creature spell into an absolute manufacturing plant. When you cast Astrid Peth, Samwise Gamgee triggers alongside her entry, and the resulting food generation is hyper-charged so that sacrificing your newly minted artifacts to Phyrexian Altar provides both the mana to recast Astrid and the exact resources needed to recur her indefinitely.