  Using Gauss-Manin derivatives of normal functions, we arrive at some
remarkable results on the non-triviality of the transcendental regulator for
$K_m$ of a very general projective algebraic manifold. Our strongest results
are for the transcendental regulator for $K_1$ of a very general $K3$ surface.
We also construct an explicit family of $K_1$ cycles on $H \oplus E_8 \oplus
E_8$-polarized $K3$ surfaces, and show they are indecomposable by a direct
evaluation of the real regulator. Critical use is made of natural elliptic
fibrations, hypersurface normal forms, and an explicit parametrization by
modular functions.
