Combination discovery

Owns a recipe graph that maps combinations of elements, usually unordered pairs, to results, the set of elements the player has found, and per-recipe discovery records. A combine action looks up the chosen inputs: if a recipe exists the result joins the player's set, first-time results are announced, and the new element becomes an input for further combinations; if none exists nothing happens or a small cost is paid. The graph is hidden, so the loop is experimentation, and progress is counted in elements found rather than items used. Infinite Craft (2024) starts from water, fire, wind, and earth and has no fixed graph: on a cache miss a language model (Llama 2, later Llama 3.1) names the result, capped at twenty tokens, with an emoji; the result is stored so every player gets the same answer, and the player who triggered it earns a First Discovery label. Little Alchemy and Doodle God use authored graphs. It differs from hand-crafting, where known recipes turn carried components into useful items at workstations, and from generative-content, which owns the model call rather than the discovery loop.

Curiosity as the whole loop. The player tries pairs on a hunch, laughs at or argues with the result, and chases rare elements by reasoning about what the designer or the model would think. Each find opens new combinations, so the field of untried ideas keeps growing.

• graph size and depth, authored or generated
• number of inputs per combination and whether order matters
• cost of a failed combination
• hint systems and whether the count of remaining recipes is shown
• shared first-discovery records and leaderboards
• whether elements have any use beyond further combination

• Without hints, players brute-force every pair or consult a list, which ends the discovery loop.
• Authored results that do not follow from their inputs feel arbitrary.
• Generated graphs drift into nonsense or offensive results and need moderation.
• Elements with no use beyond combining make the collection feel hollow once novelty fades.

• Each discovery enlarges the input set, so the number of untried pairs grows roughly with the square of elements found.
• A shared cache turns discovery into a race for First Discoveries and produces community lists of paths to rare results.
• Players form folk theories about how the graph or the model reasons and test them systematically.

• Can generated combination results carry mechanical properties that make them useful inside a simulation, rather than only names?
• What hint density keeps experimentation fun without turning it into lookup?