graeco-latin squares
an interactive visualization exploring mutually orthogonal latin squares (MOLS) and their mathematical properties. this project renders abstract mathematical constructs as dynamic visual patterns with corresponding sound generation based on mathematical relationships.
concept
graeco-latin squares explores the beauty and complexity of mathematical structures known as mutually orthogonal latin squares (MOLS). these structures, first studied by leonhard euler in the 18th century, have applications in experimental design, coding theory, and finite geometry.
this project visualizes these abstract mathematical objects as interactive color grids, where each cell's color is determined by the underlying mathematical relationships. as users interact with the visualization, algorithmically generated sounds reflect the mathematical properties being illustrated, creating a multi-sensory experience of mathematical structure.
technical details
the visualization engine uses D3.js for data-driven document manipulation and webGL for high-performance rendering of complex mathematical patterns. the audio component employs tone.js to generate sounds based on the mathematical relationships being visualized.
key mathematical concepts implemented include:
- latin square generation using finite field operations
- euler's construction for pairs of orthogonal latin squares
- macneish's theorem for constructing MOLS
- connections to projective planes and error-correcting codes
visual documentation
