Antenna current phasing

Two things are very important to understand when putting up antennas.
First the high current points like the center third of a dipole radiates most of your signal and should be high and in the clear. Low current parts radiate minimum and can be low or bent.
Also on longer wires adjacent halfwave sections are out of phase and radiation tends to cancel or at best change the radiation pattern drastically.
Knowing where the high current and low current points are is important to understanding radiation.
On a single halfwave wire the radiation is broadside.
On a full wave wire with current in one half of the wire is out of phase with current in the other half and broadside radiation is cancelled or at least significantly reduced.  The half square antenna is a good example of this. With the half square, current in the two vertical wires is in phase and adds up broadside to the antennas. Current at the center of the top wire is zero but current to either side of center is out of phase so radiation from the top wire is minimal. 
In other words the horizontally polarized radiation is reduced, while the vertical radiation from the two verticals, where the current is in phase is formed into a bidirectional beam pattern.
To see how the current is on a wire start at one end. Current is always near zero at the end of a wire. As you move back from the end the current builds up to a maximum at the 1/4 wave point.  We can call this the positive direction. Then it decreases to zero at the 1/2 wave point. As you move farther from the end the current the current builds up again but in the negative direction until it is maximum again at 3/4 wave from the end. The current at this point is completely opposite in phase with the current at the point 1/4 wave from the end. As you keep moving back from the end to one full wave the current is again zero. That describes the current distribution on a full wave length of wire. If the wire is longer than full wave the pattern just repeats. 
You can draw this picture for any wire antenna. The half square is simply one such wave length of wire. 

Here are two quick sketches showing current on the wire. I drew the diagram two ways. Basically all antenna patterns are formed by breaking the current down into small segments and considering the difference in phase relationship of each little bit of radiation. The more segments you use the more refined the pattern. Here I just crudely used 4 segments for a one wave wire.