Video: https://www.youtube.com/watch?v=KJe9H6qS82I

Nice! Lots of gliders and stable blocks, at 3:13 two gliders meet to become a spinner, at 3:20 a puffer comes along.

My god, it's full of gliders too!

Here's a Shadertoy implementation: https://www.shadertoy.com/view/XtdSDn

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) )

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 ?

Based on this paper:

https://arxiv.org/abs/1111.1567 Rafler, Stephan - Generalization of Conway's "Game of Life" to a continuous domain - SmoothLife [2011]

Citations here: https://scholar.google.com/scholar?cites=7362834692940912518

Arxiv also points to a blog post from 2013 about it:

http://www.preposterousuniverse.com/blog/2013/02/20/smooth-l...

Whose author found it via, OF COURSE, John Baez:

https://plus.google.com/u/0/117663015413546257905/posts/bguQ...

The amount of high level research-and cool new results-that continue to be found in GoL is amazing.

For some reason I assumed they were referring to the board game "LIFE" and had developed a continuous version with respect to the money (so that things weren't always in increments of $10,000). Not sure how having children would work on a continuous domain though.

They would be some sort of probability distribution.

Damn this is cool.

This is really neat, thanks for sharing.