In free space, what is the radiation pattern of a half-wave dipole?

A half-wave dipole radiates its energy primarily perpendicular, or 'broadside', to the axis of the wire. If you imagine the wire suspended in free space, the strongest part of the signal expands outward from the sides of the wire. Visually, this 3D radiation pattern looks like a large doughnut (toroid) with the wire running exactly through the center hole of the doughnut. Very little to no energy is radiated straight off the ends (the tips) of the wire, creating deep 'nulls' in those directions. Distractors claiming omnidirectional radiation or maximum radiation from the ends describe the exact opposite of how a dipole behaves. An omnidirectional pattern would mean it radiates equally in all directions horizontally, which a basic dipole does not do.