Orbifoldr: Classifying Wallpaper Groups via Functional Image Analysis in Haskell
summary
Orbifoldr is a Haskell pipeline that represents images as functions Coord -> Color, uses Conway’s orbifold notation to test symmetry by composing geometric transforms, and confines IO to JuicyPixels at the boundary. It classifies 34 benchmark images and scores 32/34 uniquely correct after tuning thresholds; failures come from stride-based sampling, sharp centers, and texture variance. Allowing gradient matches crashes precision (matching falls from 69% to 29%), and memory allocation, not CPU, limits parallel scaling.
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chapters (6)
- 0:00Orbifoldr project intro
- 2:32Wallpaper group math
- 11:00Why Haskell fits
- 15:12Pipeline for classification
- 23:04Effects and challenges
- 27:18Q&A
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