Allow me to get slightly
mathematical for a moment.
An antenna's radiation is related to the spatial convolution of the 3D free space Green's Function and the electric currents residing on the antenna.
Consider the 3D free space Green's Function G:
G = e -jkR/R
where k is the wavenumber, and R is the distance between the observation point r' and the source point r, R = |r - r'|
The radiated magnetic field H due to a vector electric current J on the antenna is:
H = ∇ x A
where A is the vector magnetic potential involving the convolution mentioned earlier:
A = (μ / 4 π) ∫s J (e
-jkR/R) ds
The radiated electric field E can be obtained from H by using the frequency-domain Maxwell's Equations thusly:
E = ∇ x H / jw ε
If you've studied fourier analysis before you might have noticed that the antenna radiation pattern is actually a spatial fourier transform of the antenna currents! That is so cool ...