Solar Powered Conways Game of Life

From https://github.com/thearn/game-of-life :

> How it's written

> The game grid is encoded as a simple m by n array (default 100x100 in the code) of zeros and ones. In each program, a state transition is determined for each pixel by looking at the 8 pixel values all around it, and counting how many of them are "alive", then applying some rules based that number. Since the "alive" or "dead" states are just encoded as 1 or 0, this is equivalent to summing up the values of all 8 neighbors.

> If you want to do this for all pixels in a single shot, this is equivalent to computing the 2D convolution between the game state array and the matrix [[1,1,1],[1,0,1],[1,1,1]]. Convolution is an operation that basically applies that matrix as a "stencil" at every position around the game grid array, and sums up the values according to the values in that stencil. And convolution can be very efficiently computed using the FFT, thanks to the Fourier Convolution Theorem.

> One side effect: the convolution using FFT implicitly involves periodic boundary conditions, so the game grid is "wrapped" around itself (like in Pacman, or Mario Bros. 2). If you wanted to change this, you would just have to modify the 2D convolution function to use an orthogonal form of the DCT instead of the FFT. This would correspond to "hard" (i.e. Dirichlet) boundary conditions on the convolution operator.

> I think you could do this with scipy using the 1D orthogonal dct provided:

  from scipy import fftpack
  fftpack.dct(data, norm='ortho')

The (Inverse) Quantum Fourier Transform is also applied in QC; https://en.wikipedia.org/wiki/Quantum_Fourier_transform#Defi...