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A270942
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 225", based on the 5-celled von Neumann neighborhood.
4
1, 4, 13, 28, 33, 84, 61, 164, 93, 244, 125, 352, 152, 505, 224, 629, 260, 848, 333, 1072, 360, 1284, 500, 1464, 536, 1832, 612, 2116, 700, 2428, 860, 2788, 1041, 3160, 1116, 3452, 1052, 3888, 1357, 4320, 1468, 4732, 1585, 5048, 1725, 5716, 1880, 6080, 2097
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=225; 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: A108753 A024970 A079430 * A272455 A220745 A298017
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 26 2016
STATUS
approved