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A271892
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 411", based on the 5-celled von Neumann neighborhood.
1
4, 4, 23, -7, 68, -45, 117, -88, 219, -203, 348, -285, 421, -332, 475, -447, 704, -665, 889, -832, 1119, -1003, 1236, -1096, 1399, -1339, 1619, -1491, 1980, -1777, 2053, -1901, 2365, -2449, 2817, -2593, 3169, -2916, 3355, -3295, 3751, -3571, 4176, -4113
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=411; 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. A271889.
Sequence in context: A075219 A264650 A272450 * A271538 A271457 A268194
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 16 2016
STATUS
approved