combinatoricsfractalsnumber theory
Pascal Triangle Patterns Mod n
Combinatorics turns into geometry
February 21, 2026 6 min read
Pascal’s triangle starts as arithmetic, but modulo arithmetic turns it into visual texture.
The core identity is inline-friendly as and expands to:
Why patterns emerge
The recurrence propagates local structure down the triangle. Modulo constraints create repeating finite states, so motifs reappear at larger scales.
For modulo 2, the familiar Sierpinski-like voids show up. Other mod values build different geometries with alternating bands, triangular islands, and near-periodic diagonals.