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A271810
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 403", based on the 5-celled von Neumann neighborhood.
1
4, 4, 19, -11, 79, -51, 111, -107, 244, -185, 277, -289, 501, -393, 437, -416, 748, -677, 801, -768, 1064, -928, 1143, -1167, 1452, -1260, 1495, -1463, 1939, -1879, 2188, -2157, 2645, -2484, 2735, -2547, 3088, -2944, 3387, -3355, 3819, -3619, 4132, -4005
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=403; 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. A271807.
Sequence in context: A272321 A272290 A271688 * A264528 A035413 A261568
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 14 2016
STATUS
approved