Lattice To Torus Interactive

Choose a complex value $\tau$ on the complex plane.

Then the lattice \(\Lambda_{\tau} = \mathbb{Z} + \mathbb{Z}\tau\) is generated by the basis $(1,\tau)$.

The quotient \(\mathbb{C}/\Lambda_{\tau}\) is obtained by identifying opposite sides of the fundamental parallelogram, giving a complex torus.