Unfortunately the demo video in the link you posted seems to be private, so I might be misunderstanding.
There are some diagonal interactions that are not directly expressible in this way, but they can propagate through the non-diagonal neighbours instead.
Thanks for reminding me.
A nice optimization trick is to make the cell buffers 2 cells wider and taller (or two times whatever the neighborhood radius is), and then before each generation you update the "gutter" by copying just the wrapped (or mirrored) pixels. Then your run the rule on the inset rectangle, and the code (in the inner loop) doesn't have to do bounds checking, and can assume there's a valid cell to read in all directions. That saves a hell of a lot of tests and branches in the inner loop.
Also, you you can define the Margolus neighborhood in terms of the Moore neighborhood + horizontal phase (even/odd column x) + vertical phase (even/odd row y) + time phase (even/odd time). With that information the rule can tell if it's at an even or odd step, and which of the four squares of the grid it's in.
That's how the CAM6 worked in hardware: it used the x/y/time phases as additional bits to determine the Margolus neighborhood lookup table index.
https://github.com/SimHacker/CAM6/blob/master/javascript/CAM...
Here's how my CAM6 emulator computes the CAM6-hardware-compatible Margolus lookup table index, based on the 9 Moore neighbors + phaseTime, phaseX, and phaseY:
function getTableIndexUnrotated(
nw, n, ne,
w, c, e,
sw, s, se,
phaseTime,
phaseX,
phaseY) {
// 0 1 2 3 4 5 6 7 8 9
// c0 c1 cw0 ccw0 opp0 cw1 ccw1 opp1 pha0 pha1
// 0x1 0x2 0x4 0x8 0x10 0x20 0x40 0x80 0x100 0x200
var cw, ccw, opp;
if (phaseTime) {
return (
// c c'
(c & 0x03) |
// cw cw'
(cw = (phaseX
? (phaseY
? (e & 0x03)
: (n & 0x03))
: (phaseY
? (s & 0x03)
: (w & 0x03))),
(((cw & 0x01) << 2) |
((cw & 0x02) << 4))) |
// ccw ccw'
(ccw = (phaseX
? (phaseY
? (s & 0x03)
: (e & 0x03))
: (phaseY
? (w & 0x03)
: (n & 0x03))),
(((ccw & 0x01) << 3) |
((ccw & 0x02) << 5))) |
// opp opp'
(opp = (phaseX
? (phaseY
? (se & 0x03)
: (ne & 0x03))
: (phaseY
? (sw & 0x03)
: (nw & 0x03))),
(((opp & 0x01) << 4) |
((opp & 0x02) << 6))) |
// pha pha'
0x200);
} else {
return (
// c c'
(c & 0x03) |
// cw cw'
(cw = (phaseX
? (phaseY
? (w & 0x03)
: (s & 0x03))
: (phaseY
? (n & 0x03)
: (e & 0x03))),
(((cw & 0x01) << 2) |
((cw & 0x02) << 4))) |
// ccw ccw'
(ccw = (phaseX
? (phaseY
? (n & 0x03)
: (w & 0x03))
: (phaseY
? (e & 0x03)
: (s & 0x03))),
(((ccw & 0x01) << 3) |
((ccw & 0x02) << 5))) |
// opp opp'
(opp = (phaseX
? (phaseY
? (nw & 0x03)
: (sw & 0x03))
: (phaseY
? (ne & 0x03)
: (se & 0x03))),
(((opp & 0x01) << 4) |
((opp & 0x02) << 6))) |
// pha pha'
0x100);
}
};