q-Expansion Visualization
q = e2πiτ
τ-Plane (Input)
Complex Upper Half-Plane (τ = x + iy)
q-Plane (Output)
Punctured Unit Disk (q = r · eiθ)
Function q-Expansion
You are now visually designing a complex function. The gradient map shows the output of this function. By moving the sliders, you are placing "poles" (sources) and "zeros" (sinks) onto the map, watching the entire landscape warp in real-time.
f(q) = ... + c-1q-1 + c0 + c1q + c2q2 + ...