Some of the decisions in Dominion are made by the player, e.g. which card to play, buy, or gain. What rules should we make regarding these decisions? Below I will outline a basic Touring machine in Dominion, where these choices are dictated by a set of instructions, i.e., not rooted in the rules of Dominion.
The basic idea is to use the deck and the hand of the player as storage (Copper and Silver as 0 and 1, and Gold as blank). Keeping track of the order in which you drew the cards to decide which one is currently active (the last one you drew). The underlying method to work on the storage uses the following algorithm:
Kingdom: Overlord, Crown, Mandarin, Watchtower, Ambassador, Smuggler, Lurker, Treasure Map, Smithy, Pawn
Setup: Mandarin in trash, Watchtower and 6 Overlords (OL) in hand, in the previous turn, I gained a Copper, Silver, and Gold
OL1 as Crown
... OL2 as Crown
... ... OL3 as Crown
... ... ... OL4 as Crown
... ... ... ... OL5 as Crown
... ... ... ... ... OL6 as Treasure Map, trash OL6
... ... ... ... ... OL6 as Lurker, gain/trash Mandarin, put OL1-5 on deck
... ... ... ... OL5 as Lurker, gain OL6 on deck
... ... ... OL4 as Smithy, draw OL1-3
... ... OL3 as Smithy, draw OL4-6
... OL2 as X
The important part of this algorithm is that it keeps the hand unmodified and allows to play one action X every cycle. To implement the Turing machine, we can modify the currently active card using X = Pawn or X = Mandarin by adding another card to our hand or putting the active one back on the deck. Overwriting the storage depends on the cards used to store the information. Writing is a combination of returning the old card with X = Ambassador, gaining a new card with X = Smuggler, watchtowering it on top of the deck, and then drawing it with X = Pawn.