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Lambda Screen: Fractals in Pure Lambda Calculus
Lambda Screen allows you to draw images using terms of pure lambda calculus. By using fixed-point combinators, you can even create infinitely detailed fractals.
Wrapped in monadic IO, lambda calculus provides a great interface for computation – as can be seen in user-friendly syntactic variants like my programming language bruijn. For lambda screen we can interpret this as a recursive split into smaller squares, where in each iteration one of the quadrants (depending on its position) gets drawn as black. The Cantor dust is another great example of how infinitely detailed structures appear as unreduced (grey) quadrants when reduction inevitably gets halted.
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