SmoothLife uses two disks around each point to determine the instantaneous rate of change. Inside each disk the values are summed. This is a convolution with a disk filter.
http://en.wikipedia.org/wiki/Convolution
As it says on that page, FFT is often used for convolution because it is fast: after applying a discrete Fourier transform to the kernel and the image, the resulting images must only be multiplied together before applying an inverse FFT.