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A272110
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 427", based on the 5-celled von Neumann neighborhood.
1
4, 8, 19, 5, 52, -9, 65, -32, 179, -123, 188, -113, 337, -288, 395, -291, 572, -497, 633, -520, 891, -803, 948, -793, 1241, -1160, 1347, -1163, 1668, -1561, 1777, -1584, 2179, -2059, 2284, -2049, 2721, -2608, 2875, -2611, 3340, -3201, 3497, -3224, 4043
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=427; 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. A271902.
Sequence in context: A351323 A104137 A308563 * A272542 A280114 A162362
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 20 2016
STATUS
approved