Rat Explorer

A rational tile (rat) is a closed matchstick polygon on the chosen cyclotomic ring ℤ[ζ_n]: a boundary of unit-length edges with turn angles in integer multiples of 360°/n. We trace it turtle-style - starting at the origin facing direction 0, each angle turns the facing direction by that many ring units before we step one unit forward. A partial, not-yet-closed sequence is a snake.

To inspect a polygon, enter a whitespace-separated angle sequence, e.g. the Spectre tile (click to load): 3 2 0 2 -3 2 3 2 -3 2 3 -2 3 -2

To build one interactively:

• ←/→ select angle
• ↑ confirm angle
• ↓ undo last angle
• Esc clear edge preview
• Mobile: swipe horizontally to select, vertically to confirm / undo.

When the polygon is closed, the panel shows additional statistics and normal forms for the resulting rat.