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A273710
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 873", based on the 5-celled von Neumann neighborhood.
1
3, 17, 12, 35, 37, 39, 49, 84, 52, 80, 24, 135, 57, 135, 57, 196, 92, 172, 92, 184, 108, 180, 152, 212, 92, 292, 116, 320, 100, 256, 172, 328, 224, 284, 204, 340, 120, 332, 296, 328, 248, 328, 304, 356, 328, 268, 376, 440, 232, 472, 192, 692, 64, 572, 224
OFFSET
0,1
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=873; 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}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)
CROSSREFS
Cf. A273707.
Sequence in context: A088122 A357373 A273702 * A087964 A372798 A174182
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 28 2016
STATUS
approved