so regarding relativistic SmoothLife, I had this idea:
In non-relativistic SmoothLife we integrate over two subsets of Euclidean space, the disk and the ring, with radiuses defined according to a Euclidean metric dr^2 = dx^2 + dy^2.
If the time dimension were also Euclidean we could simply extend the integration to all past times with "time radiuses" defined according to a metric dr^2 = dx^2 + dy^2 + dt^2.... read more
Idea alert! Wouldn't it be nice, if SmoothLife were Lorentz invariant?
Like Konrad Zuse said in his paper "rechnender Raum" (calculating space), the first objection from physicists against cellular automaton based physics is always, that it isn't Lorentz invariant. But then, he says, we have to think of ways how we could MAKE it Lorentz invariant, and not simply write it off. See, that's the attitude I like. Maybe now with the SmoothLife model where we have a PDE, and no grid (at least theoretically), this would help to make a step in this direction.... read more
Just had an idea how to modify snm in an interesting way, in order to get "the good stuff back" from GoL. What if we take our usual snm and put a filter over it, letting through only the stuff at integer positions and setting to 0 the stuff in between?
So, for instance one could define a 2D gaussian bump at positions n,m in snm such that if we take
(gaussian(3,0) + gaussian(2,1) + gaussian (3,1))*snm... read more
In my presentation I listed the idea of a glider constructor as a "research topic". When I put this up it was true, but then I implemented it not long afterwards. The reason was, that I was searching for a 3D glider then, and I wanted to be able to draw a shape that I had in mind and see if it works, at least approximately. The point is that I didn't want to draw the whole shape, but only one half of the profile. The rotational symmetry then would be calculated automatically and give the whole 3D glider.... read more
Concerning the search for the generic smooth time stepping mode, I came up with an intriguing idea today which nonetheless failed, as of yet. Remember that like in the original GoL for SmoothLife with discrete time stepping we consider snm the new function value for each time step. So for snm to be an additive value one has to consider the analog in the original GoL first! That was my idea today. I haven't tried it explicitly, but it is straightforward. Just imagine instead of setting cells to 0 or 1, subtracting or adding 1 appropriately. These would be the rules of additive GoL:... read more
Kellie Michele Evans - Larger than Life
Marcus Pivato - RealLife
Chapter 12 in "Game of Life Cellular Automata", Andrew Adamatzky, Springer 2010
Bruce MacLennan - Continuous Spatial Automata
Leon Chua - Cellular Neural Networks
http://en.wikipedia.org/wiki/Cellular_neural_network... read more
just found a new time stepping mode. now we've got three to choose from (not counting the delayed time and the acceleration modes, which I consider very experimental, and which are not included in the source code).
mode 0 (discrete)
f(x,t+1) = S[snm] f(x,t)
mode 1 (smooth)
f(x,t+dt) = f(x,t) + dt S[snm'] f(x,t) with snm' = 2*snm-1
this becomes in the limit dt->0 in the Euler integration sense
d_t f(x,t) = S[snm'] f(x,t)... read more
"Didn't you just implement RealLife from Pivato?", I hear you ask. Well, no I didn't, because RealLife can not be run on a computer. Pivato himself says so. I consider RealLife a special case of SmoothLife for inner radius going to zero. With this notion it is clear that RealLife can never be simulated on any finite grid/lattice/mesh, because as soon as the inner radius approaches the grid spacing, it is over. You have to do some smoothing/mean field approximation for the inner point. Then you can let the outer radius go to infinity. But as it turns out, you don't need a very small inner radius, it makes no qualitative difference. Even with inner radius one third of outer radius the glider looks basically the same as you can see if you compare the generic smooth glider with the bugs of LtL. RealLife is a theoretical, mathematical model. SmoothLife has the advantage that it can also be run on a computer. And we have to be able to experiment, don't we?
Welcome to the SmoothLife developer Blog!
Be sure to check out
especially the SmoothLife playlist
and especially the presentation therein.
You may have guessed it, but SmoothLife is not the first Game of Life implementation I ever wrote. I could show you a Game of Life implementation I wrote in Assembler on the Commodore Amiga from 1992 that uses the graphics co-processor called Blitter that the Amiga had (already in 1985). So, GoL for me always was linked to image processing.... read more