Conway's Game of Life, being discretized in both space and time domains, has no locally conserved quantities. SmoothLife, however, is a generalization of the Game of Life to a continuous and spatially-isotropic domain. The evolution rules of SmoothLife are explicitly defined in terms of integrals over space and time, so it would therefore seem that it should fulfill the preconditions of Noether's theorem (i.e., having differentiable symmetries) to imply conserved quantities analogous to energy (from continuous time-translation symmetry), linear momentum (from space translation symmetry), and angular momentum (from rotational symmetry).
Just from observing a SmoothLife simulation, though, it is not at all obvious what exactly is being conserved, if anything, as the simulation progresses. So, what exactly are the conserved quantities of SmoothLife "physics"?--or have I missed something, and there actually aren't any?
