OFFSET
0,1
COMMENTS
The rule turns a cell to ON at step n if an even, nonzero number of its eight neighbors were ON in the previous. For example, at n=2 the cell (0,0) is ON because the two neighbors (-1,0) and (0,-1) and no others were ON at the previous step.
It appears that whenever n is divisible by 3, there is a visible disjoint 2x2 square leading the automaton in each cardinal direction.
EXAMPLE
For n=3, the configuration includes the initial four ON cells plus four other 2 X 2 squares in each cardinal direction.
MATHEMATICA
m = 100; n = 2 m + 1;
A = Table[0, {p, 1, m}, {q, 1, n}, {z, 1, n}];
A[[1, m, m + 1]] = 1;
A[[1, m, m]] = 1;
A[[1, m + 1, m + 1]] = 1;
A[[1, m + 1, m]] = 1;
For[i = 2, i <= m, i++,
For[x = 2, x <= n - 1, x++,
For[y = 2, y <= n - 1, y++,
sum = A[[i - 1, x - 1, y - 1]] +
A[[i - 1, x, y - 1]] +
A[[i - 1, x + 1, y - 1]] +
A[[i - 1, x - 1, y]] +
A[[i - 1, x + 1, y]] +
A[[i - 1, x - 1, y + 1]] +
A[[i - 1, x, y + 1]] +
A[[i - 1, x + 1, y + 1]];
A[[i, x, y]] = If[sum > 0, 1 - Mod[sum, 2], 0];
]
]
];
Table[Plus @@ Plus @@ A[[i, All, All]], {i, 1, m}]
(* Kellen Myers, Feb 07 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Kellen Myers, Feb 06 2015
STATUS
approved