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A273410
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 694", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 21, 33, 45, 53, 85, 117, 141, 169, 205, 241, 261, 293, 377, 453, 505, 569, 633, 705, 753, 821, 925, 1021, 1085, 1161, 1261, 1345, 1389, 1445, 1633, 1797, 1905, 2041, 2161, 2305, 2409, 2549, 2709, 2877, 2997, 3145, 3301, 3457, 3557, 3685, 3921, 4141
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=694; 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: A269523 A319384 A211427 * A273486 A146867 A068481
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 21 2016
STATUS
approved