Energetic particle irradiation of solids can cause surface ultra-smoothening, self-organized nanoscale pattern formation in surface topography or bulk composition, or degradation of the structural integrity of nuclear reactor components. Here we report a study of the patterns formed on argon ion sputtered Si surfaces at room temperature as a function of the control parameters ion energy and incidence angle.  We identify regions in control parameters space where holes, parallel mode ripples and perpendicular mode ripples form, and a region where the flat surface is stable.  In the vicinity of the boundaries between the stable and pattern forming regions, called bifurcations, we follow the time dependence from exponential amplification to saturation and examine the amplification rate and the wavelength in the exponential amplification regime. The resulting power laws are consistent with the theory of nonequilibrium pattern formation for a Type I (constant-wavelength) bifurcation at low angles and for a Type II (diverging wavelength) bifurcation at high angles. We discuss the failure of all sputter rippling models to adequately describe these aspects of the simplest experimental system studied, consisting of an elemental, isotropic amorphous surface in the simplest evolution regime of linear stabilty.