The Gaussian function takes the general form of:

[tex] f(x) = Ae^\frac{-(x-b)^2}{c^2}[/tex]

Further yet, the antiderivative of this function is the famous error function erf(x).

What I'd like to know is... what is the magic behind this equation. Why is it able to describe so much real world phenomena. Can it be derived or what was Mr. Gauss thinking when he came up with this.

Is there anything else I missed about the magic of this function?