Lambda Calculus Tutorials

Tiling with Lambda Calculus

Learn how to model spatial transformations and recursive patterns using lambda abstractions and functional recursion.

What is Tiling in Lambda Calculus?

Tiling involves generating spatial patterns through recursive function applications. In lambda calculus, this is achieved using higher-order functions to represent transformations and spatial rules. These concepts form the foundation for creating algorithmic visuals and spatial computation models. 

-- Recursive tile function
tile = λn.λx.λy. 
    if (mod x 2) == 0 
      then colorRed 
      else if (mod y 2) == 0 
           then colorBlue 
           else colorGreen

* This example checks coordinate parity to assign colors to tiles.

Visual Pattern Generation

This 8-tile grid illustrates how lambda calculus functions can generate color patterns based on coordinate functions.

Try a Custom Pattern

Enter a simple tiling rule to see how lambda calculus generates spatial patterns.

Result will appear here (example: alternating red and blue tiles)

Advanced Tiling Patterns

Build recursive tiling models with SKI combinators and explore fractal generation using pure lambda abstractions.

🧩 Explore Advanced Patterns
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