Functional geometry: picture combinators and recursive fish
summary
Implements Henderson’s 2002 “functional geometry” approach in F# with Fable, treating pictures-as-functions and composing them with four basic transforms (turn, flip, toss, scale) plus combinators above/beside to build larger images. Builds a nine-piece no-net and recursive side/corner combinators that assemble Escher’s square limit, the demo compiles and renders the fractal-like tiling though hot-reload sometimes lags; source is published for reproduction.
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chapters (9)
- 0:00Introduction and agenda
- 2:24Core abstraction: pictures as functions
- 6:21Basic transformations: turn, flip, and toss
- 18:08Combining pictures: above and beside
- 26:34Building larger structures: quarter and net
- 33:58Recursive compositions: fish and tiles
- 41:00Square limit: corners and sides
- 45:36Final result and color variations
- 48:30Conclusion and resources
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