What type of radiation pattern is created by two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed in phase?

When two antennas are fed perfectly in phase (with a 0-degree phase difference), their signals will always combine constructively at any point that is equidistant from both antennas. The entire plane perpendicular to the line connecting the antennas—the broadside direction—is equidistant. Along the axis connecting the two antennas, the physical spacing of 1/2-wavelength comes into play. A signal from one antenna must travel 180 electrical degrees to reach the other. Since they are fed in phase, the arriving signal will be 180 degrees out of phase with the signal radiating from the second antenna, causing total cancellation along the array axis. With maximum radiation shooting outward perpendicularly and total nulls occurring directly along the line of the antennas, the resulting shape is a figure-eight pattern broadside to the axis of the array.