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Comment by ttoinou | Hacker News Reader

The FFT version is interesting

   G∗K == F⁻¹( F(G)·F(K) )

So if we iterate t times (as in t step in time) this do we get this formula (convolution product being associative) ?

   ((G∗K)*K)*K ... t time = G∗K^t == F⁻¹( F(G)·F(K^t) )

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No, because the transition function has to be applied at each time step as well as the convolution. In the source code, that's

    self.rules.s(N_buffer, M_buffer)

Okay thanks ! Makes it more interesting. I like it when it's doing something in one space (fourier space here) then something else in another space (original space) and you have to switch between multiple point of view to make something awesome (a fractal for example)

Hmm... I now wonder if it'd make sense to make a version of this that uses Constant Q instead of Fourier transforms...

...and I also wonder why this still uses a square lattice on the bottom layer - shouldn't a continuous version permit the use of a hexagonal lattice, which doesn't work that well within the discrete domain (although people have attempted it not that unsuccessful, but it still had issues.)

If you assume K is unchanging, yes. Like if it were a fixed point on the board.

The kernel doesn't change in Smooth Life, right ?

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