Maths for Programming, Fun, and Creativity
summary
Maths-as-abstraction proves practical: algebraic Monoids with identity and associativity let different domains share the same reduce logic, enabling parallel folds, CRDTs (commutative idempotent monoids) and foldMap-based MapReduce. Concrete demos include audio synthesis by summing harmonics (sawtooth from 100 harmonics), procedural graphics from Lindenmayer turtle programs producing fractals (L-systems yielding Koch snowflake and dragon curve), and tile-based game worlds (144 tiles on NES with 2KB RAM). Each demo renders and sounds as expected, showing the abstractions compose and scale.
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chapters (7)
- 0:00Start
- 4:23Counting, numbers, ratios?
- 13:41Sawtooth Wave
- 15:36Abstractions inspire creativity
- 17:00What about programming?
- 24:17Composing abstractions
- 29:19Lindenmayer Systems
