Oatmeal is Cheap: A Fundamental Theorem for Procedural Generators
summary
A provable link ties a generator’s compressed source length to the size of its possibility space and to the maximum artifact complexity so three simple inequalities bound what a generator can do The paper frames uncoded knowledge as the human cost to add structure and shows increasing scale without increasing that cost yields “oatmeal” sameness Examples include why adding villages to Minecraft forces extra engineering why Borderlands‑style scale tends toward repetition and rough estimates for Wikipedia and Stable Diffusion’s unique outputs
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chapters (18)
- 0:00Procedural content intro
- 3:01PCG myths and challenges
- 8:19PCG math perspective
- 10:04Ideal generators defined
- 12:35Measuring generator length
- 15:23Possibility space and scale
- 17:30Cograph complexity intro
- 21:02Generator constraints graph
- 22:04Complexity vs possibility space
- 23:29Knowledge vs possibility space
- 24:32Upper bound on generator length
- 27:47Minecraft Village theorem
- 31:19T Garden case study
- 33:28Industry pressure and oatmeal
- 36:17Fundamental theorem of PCG
- 37:01Approximating large generators
- 39:53Stable diffusion outputs
- 41:39Conclusion
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