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A271008
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 246", based on the 5-celled von Neumann neighborhood.
4
1, 5, 8, 24, 28, 48, 36, 108, 68, 132, 136, 224, 172, 276, 276, 344, 308, 496, 408, 548, 560, 652, 604, 860, 688, 1032, 824, 1144, 972, 1256, 1224, 1432, 1356, 1696, 1392, 1836, 1716, 2016, 1828, 2144, 2152, 2496, 2080, 2632, 2556, 2948, 2708, 3248, 3088
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=246; 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: A253078 A270185 A169701 * A272577 A140113 A357117
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 28 2016
STATUS
approved