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A271121
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 286", based on the 5-celled von Neumann neighborhood.
4
1, 5, 12, 17, 37, 28, 76, 45, 112, 72, 153, 121, 204, 145, 301, 196, 344, 277, 404, 360, 497, 372, 632, 489, 740, 536, 849, 681, 1008, 672, 1141, 893, 1248, 940, 1473, 1101, 1592, 1180, 1741, 1405, 1924, 1468, 2121, 1637, 2356, 1728, 2513, 2013, 2748, 2072
OFFSET
0,2
COMMENTS
Initialized with a single black (ON) cell at stage zero.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=286; stages=128;
rule=IntegerDigits[code, 2, 10];
g=2*stages+1; (* Maximum size of grid *)
a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca=a;
ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k=(Length[ca[[1]]]+1)/2;
ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
CROSSREFS
Sequence in context: A063297 A237669 A022137 * A271301 A282696 A314288
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 31 2016
STATUS
approved