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

0,1

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.

Links

Table of n, a(n) for n=0..99.

Index entries for sequences related to cellular automata

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

Cf. A160239.

Sequence in context: A083504 A277291 A362212 * A368903 A291548 A212019

Adjacent sequences: A254728 A254729 A254730 * A254732 A254733 A254734

Keyword

nonn

Author

Kellen Myers, Feb 06 2015

Status

approved