Group Multiplication Explorer (2D)

This 2D simulator draws the Cayley graph of a finite group — cyclic ℤₙ or dihedral Dₙ — and makes every interaction a real group-theory operation rather than a cosmetic animation. Clicking one element then another looks up their true product using the group's own multiplication law (modular addition for ℤₙ; the reflection relation s·r·s = r⁻¹ for Dₙ), and switching to subgroup mode highlights the actual cyclic subgroup generated by whichever element you click, with its order always dividing the group's order exactly as Lagrange's theorem guarantees.