Kuen Surface Parametric Equation:

{2*Cosh[v]*(Cos[u] + u*Sin[u]), 2*Cosh[v]*(-u*Cos[u] + Sin[u]), v - (2*Sinh[v]*Cosh[v])} / (Cosh[v]^2 + u^2)

In the above plot, the boundaries are {u,-4,4}, {v,-3.75,3.75}. u controls the left/right symmetric wrap. v controls top/bottom. When u is large, the surface wraps in a spiral inwards and upwards.