Here is the basic equation for the gaussian equation or normal distribution.  x is the value of the variable and s is the standard deviation; μ is the mean and σ is the standard deviation.

Here is a plot of the basic normal distrubtion with μ = 0 and σ=1.

Below is the difference of gaussians.  In both gaussians, μ = 0, however the σ's are different fro the two eqautions which allows the different not to sum to 0.  In the first case, the first gaussian will have a σ = 1/2 and the second gaussian will have a σ= 2.  Then the ratios will be changed gradually until the ratio is reversed.

Below is a 2-dimensional gaussian function.