A254731 Number of ON cells in the even-rule cellular automaton after n steps with the Moore neighborhood (8 neighbors), with minimal nontrivial symmetric initial state (0,0), (0,1), (1,0), and (1,1) ON.

4, 8, 24, 20, 32, 68, 48, 72, 116, 88, 104, 140, 188, 160, 284, 272, 268, 320, 372, 352, 496, 488, 524, 608, 556, 628, 692, 820, 764, 808, 864, 976, 1024, 920, 1032, 1228, 1188, 1256, 1408, 1496, 1488, 1564, 1584, 1712, 1752, 1708, 1888, 2148, 2040, 2100, 2308, 2392, 2544, 2480, 2760, 2752, 2764, 3064, 3020, 2976, 3516, 3440, 3560, 3580, 3804, 3816, 3916, 4236, 4492, 4340, 4516, 4512, 4984, 4764, 5004, 4880, 5116, 5716, 5540, 5560, 5564, 5840, 6200, 6368, 6280, 6668, 6880, 6908, 6960, 7600, 7388, 7396, 8028, 7832, 8332, 8152, 8268, 8928, 8708, 9144

Offset: 0

Author

Kellen Myers, Feb 06 2015

Keywords

• nonn

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.

Examples

			For n=3, the configuration includes the initial four ON cells plus four other 2 X 2 squares in each cardinal direction.
		

Links

• Index entries for sequences related to cellular automata

Crossrefs

Cf. A160239.

Programs

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 *)