Functional Geometry in Swift & SwiftUI
summary
Implements Henderson’s 1982/2002 picture language almost letter‑for‑letter in Swift and SwiftUI, using SwiftUI container views and a result builder to express combinators like beside and above, plus a special rotate45 that breaks the frame. Builds F, fish, quartet, cycle and the iterative corner/side replacement that converges toward Henderson’s square limit. Offers two rendering paths: SwiftUI views for composition and a Metal shader for per‑pixel fills on the GPU. The demo runs and reproduces Henderson’s fish tilings and symmetries.
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chapters (10)
- 0:00Introduction
- 2:12Why iOS developers need functional programming
- 7:57SwiftUI as FP tool
- 15:47Functional geometry intro
- 20:09Painter abstraction in SwiftUI
- 22:42Basic transformations
- 26:18Refining combinators
- 28:07Building fish shape
- 31:26Escher Square Limit
- 33:13Summary
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