Shrinking Fish: A Functional Programmer looks at SwiftUI
summary
Reimplements Henderson’s 1982 functional geometry inside SwiftUI, treating shapes as point -> Bool functions, combining them with custom combinators like beside/above and packing those into a result-builder style API. Uses Metal shader rasterization to color pixels from those predicates, supports rotate/flip/ratio-scaled beside operations, quartet/cycle/nonet tilings and algebraic rotation rules. Produces working Square Limit–style fish tilings in SwiftUI; the implementation runs and renders the nested shrinking fish.
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chapters (11)
- 0:00Functional programming in iOS
- 3:04Understanding SwiftUI circles
- 5:23Functional shapes in Swift
- 7:11Combining and rendering shapes
- 11:27Functional geometry origins
- 14:14Implementing the picture language
- 16:48SwiftUI combinators
- 19:45Advanced composition rules
- 23:38Scaling and rotating views
- 25:16Creating the Escher fish
- 29:18The final square limit
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